(a) The value of X that makes the two alternatives equally desirable.

Question

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Answer 1

Question

Chapter 9, Problem 61P

To determine

(a)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I).

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable.

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$230$ for $EUABB$

$12%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−221.92=230−1200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=9.23 years$ .

Conclusion:

Therefore, the value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

To determine

(b)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Explanation of Solution

Given:

B’s annual benefit is $$280$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$280$ for $EUABB$

$12%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−221.92=280−1000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=5.13 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

To determine

(c)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Explanation of Solution

Given:

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−211.03=230−1000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.73 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

To determine

(d)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$

B’s annual benefit is $$280$

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−211.03=280−1200(A/P,10%,X)261.03=1200(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.45 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

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Answer 2

Question

Chapter 9, Problem 61P

To determine

(a)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I).

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable.

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$230$ for $EUABB$

$12%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−221.92=230−1200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=9.23 years$ .

Conclusion:

Therefore, the value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

To determine

(b)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Explanation of Solution

Given:

B’s annual benefit is $$280$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$280$ for $EUABB$

$12%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−221.92=280−1000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=5.13 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

To determine

(c)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Explanation of Solution

Given:

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−211.03=230−1000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.73 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

To determine

(d)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$

B’s annual benefit is $$280$

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−211.03=280−1200(A/P,10%,X)261.03=1200(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.45 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

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Answer 3

Question

Chapter 9, Problem 61P

To determine

(a)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I).

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable.

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$230$ for $EUABB$

$12%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−221.92=230−1200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=9.23 years$ .

Conclusion:

Therefore, the value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

To determine

(b)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Explanation of Solution

Given:

B’s annual benefit is $$280$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$280$ for $EUABB$

$12%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−221.92=280−1000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=5.13 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

To determine

(c)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Explanation of Solution

Given:

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−211.03=230−1000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.73 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

To determine

(d)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$

B’s annual benefit is $$280$

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−211.03=280−1200(A/P,10%,X)261.03=1200(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.45 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

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Answer 4

Question

Chapter 9, Problem 61P

To determine

(a)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I).

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable.

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$230$ for $EUABB$

$12%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−221.92=230−1200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=9.23 years$ .

Conclusion:

Therefore, the value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

To determine

(b)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Explanation of Solution

Given:

B’s annual benefit is $$280$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$280$ for $EUABB$

$12%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−221.92=280−1000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=5.13 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

To determine

(c)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Explanation of Solution

Given:

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−211.03=230−1000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.73 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

To determine

(d)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$

B’s annual benefit is $$280$

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−211.03=280−1200(A/P,10%,X)261.03=1200(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.45 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

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Answer 5

Chapter 9, Problem 61P

To determine

(a)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I).

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable.

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$230$ for $EUABB$

$12%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−221.92=230−1200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=9.23 years$ .

Conclusion:

Therefore, the value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

To determine

(b)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Explanation of Solution

Given:

B’s annual benefit is $$280$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$280$ for $EUABB$

$12%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−221.92=280−1000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=5.13 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

To determine

(c)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Explanation of Solution

Given:

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−211.03=230−1000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.73 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

To determine

(d)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$

B’s annual benefit is $$280$

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−211.03=280−1200(A/P,10%,X)261.03=1200(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.45 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Answer 6

Chapter 9, Problem 61P

To determine

(a)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I).

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable.

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$230$ for $EUABB$

$12%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−221.92=230−1200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=9.23 years$ .

Conclusion:

Therefore, the value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Answer 7

Chapter 9, Problem 61P

To determine

(a)

The value of $X$ that makes the two alternatives equally desirable.

Answer 8

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

B’s first cost is $$1200$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost.

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I).

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable.

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$230$ for $EUABB$

$12%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−221.92=230−1200(A/P,12%,X)221.92=1200(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=9.23 years$ .

Conclusion:

Therefore, the value of $X$ that makes the two alternatives equally desirable is $9.23 years$ .

Answer 13

To determine

(b)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Explanation of Solution

Given:

B’s annual benefit is $$280$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$280$ for $EUABB$

$12%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−221.92=280−1000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=5.13 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Answer 14

To determine

(b)

The value of $X$ that makes the two alternatives equally desirable.

Answer 15

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

B’s annual benefit is $$280$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $12%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.12(1+0.12)5(1+0.12)5−1)=800×0.2777=221.92$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$221.92$ for $EUACA$ , $$280$ for $EUABB$

$12%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−221.92=280−1000(A/P,12%,X)271.92=1000(0.12(1+0.12)X(1+0.12)X−1)$

Calculate the value of $X$

$X=5.13 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $5.13 years$ .

Answer 20

To determine

(c)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Explanation of Solution

Given:

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−211.03=230−1000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.73 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Answer 21

To determine

(c)

The value of $X$ that makes the two alternatives equally desirable.

Answer 22

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1000$ for $A$ in Equation (II)

$230−211.03=230−1000(A/P,10%,X)211.03=1000(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.73 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.73 years$ .

Answer 27

To determine

(d)

The value of $X$ that makes the two alternatives equally desirable.

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Explanation of Solution

Given:

B’s first cost is $$1200$

B’s annual benefit is $$280$

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .

Substitute, $$230$ for $EUABA$ , $$211.03$ for $EUACA$ , $$280$ for $EUABB$

$10%$ for $i$ and $1200$ for $A$ in Equation (II)

$230−211.03=280−1200(A/P,10%,X)261.03=1200(0.10(1+0.10)X(1+0.10)X−1)$

Calculate the value of $X$

$X=6.45 years$ .

Conclusion:

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Answer 28

To determine

(d)

The value of $X$ that makes the two alternatives equally desirable.

Answer 29

Expert Solution

Answer to Problem 61P

The value of $X$ that makes the two alternatives equally desirable is $6.45 years$ .

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given:

B’s first cost is $$1200$

B’s annual benefit is $$280$

$MARR$ is $10%$ .

Concept used:

Write the expression to calculate the equivalent uniform annual cost

$EUAC=A(A/P,i,n)$ ...... (I)

Here, the amount is $A$ , rate of interest is $i$ and time period is $n$ .

Calculation:

Calculate the equivalent uniform annual cost for $A$ .

Substitute, $800$ for $A$ , $10%$ for $i$ and $5$ for $n$ in Equation (I)

$EUAC=800(A/P,12%,5)=800(0.10(1+0.10)5(1+0.10)5−1)=800×0.2637=211.03$

To make both the alternatives equally desirable,

$(EUAB−EUAC)A=(EUAB−EUAC)B(EUAB−EUAC)A=(EUAB−A(A/P,i,n))B$ ...... (II)

Here, equivalent uniform annual benefit is $EUAB$ , equivalent uniform annual cost is $EUAC$ , amount is $A$ , interest rate is $i$ and time period is $n$ .