Engineering Economy
Engineering Economy
8th Edition
ISBN: 9781259683312
Author: Blank
Publisher: MCG
Question
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Chapter 10, Problem 40P

(a):

To determine

Calculate the rate of return by considering the MARR equal to cost of equity capital.

(a):

Expert Solution
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Explanation of Solution

Type 1: Debt (D) is 20%. Equity (E) is 80%. Cost of equity capital (CI) is 7.5%. Cost of debt capital (DI) is 10%.

Type 2: Debt (D) is 50%. Equity (E) is 50%. Cost of equity capital (CI) is 7.5%. Cost of debt capital (DI) is 10%.

Type 3: Debt (D) is 60%. Equity (E) is 40%. Cost of equity capital (CI) is 7.5%. Cost of debt capital (DI) is 10%.

Investment (IN) is $600,000. Net cash flow (NC) is $90,000. Time (n) is 7.

Rate of return (i) can be calculated using the following formula:

NI×D=NC((1+i)n1i(1+i)n)        (1)

Substitute the respective values in Equation (1) to calculate the rate of return for plan 1.

6,000,000×0.8=90,000((1+i)71i(1+i)7)480,000=90,000((1+i)71i(1+i)7)((1+i)71i(1+i)7)=480,00090,000((1+i)71i(1+i)7)=5.3333

Substitute i as 7% by trial and error method in the above calculation.

((1+0.07)710.07(1+0.07)7)=5.3333(1.605810.07(1.6058))=5.3333(0.60580.1124)=5.33335.3897>5.3333

The calculated present value factor to the annual value is greater than the actual value of 5.3333. Thus, increase the i to 7.3%.

((1+0.073)710.073(1+0.073)7)=5.3333(1.637610.073(1.6376))=5.3333(0.63760.1195)=5.33335.33565.3333

The calculated present value factor to the annual value is nearly equal to the actual value of 5.3333. Thus, cost of capital is verified as 7.3%.

The MARR is equal to the cost of debt capital. Thus, it is 7.5%. The project is accepted if the rate of return is greater than the MARR. Since the rate of return is less than the MARR, type 1 should not be selected.

Table 1 shows the rate of return that is obtained using Equation (1) and the selection decision.

Table -1

TypeRate of returnMARRDecision
17.3%7.5%Reject
222.93%7.5%Select
332.18%7.5%Select

(b):

To determine

Calculate the weighted average cost of capital.

(b):

Expert Solution
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Explanation of Solution

Weighted average cost of capital (WAC) can be calculated using the following formula:

WAC=D(DI)+(E)(CI)        (2)

Substitute the respective values in Equation (2) to calculate the weighted average cost of capital for type 1.

WAC=D(DI)+(E)(CI)=0.2(0.1)+0.8(0.075)=0.02+0.06=0.08

Weighted average cost of capital is 8%.

Table 2 shows the weighted average cost of capital, which is equal to MARR that is obtained using Equation (2) and the selection decision.

Table -2

TypeRate of returnMARRDecision
17.3%8%Reject
222.93%8.75%Select
332.18%9%Select

(c):

To determine

Calculate half of the weighted average cost of capital and cost of equity capital.

(c):

Expert Solution
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Explanation of Solution

Half of the weighted average cost of capital and cost of equity capital (MARR) can be calculated using the following formula:

MARRA=WACA+iA2        (3)

Substitute the respective values in Equation (3) to calculate the MARR for type 1.

MARR=0.08+0.0752=0.1552=0.0775

MARR is 7.75%.

Table 3 shows the MARR that is obtained using Equation (3) and the selection decision.

Table -2

TypeRate of returnMARRDecision
17.3%7.75%Reject
222.93%8.125%Select
332.18%8.25%Select

From Tables 1 to 3, it is known that type 1 gets rejected and type 2 and type 3 are accepted.

(d):

To determine

Calculate half of the weighted average cost of capital and cost of equity capital.

(d):

Expert Solution
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Explanation of Solution

These three analyses revealed that highly leveraged investment option types 2 and 3 are accepted. Thus, the answer for this question is yes.

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