
(a):
Compare the projects based on the present worth.
(a):

Explanation of Solution
Plan A: The initial cost (C) is $1,000,000 per year.
Plan B: It is a two-year contract. The cost (C) is $600,000 per semiannual starts with immediate. No payment required in the second year.
Plan C: It is a three-year contract. The cost (C) is $1,500,000 now and the second payment (C1) is $500,000 after two years.
To compare the projects, all projects’ life time should be equal. Thus, all the projects’ cash flow converts to 6 years.
Interest rate (i) is 6% per year that is compounded semiannually. Interest calculated time period (Ci) is 2. The effective interest rate per year (Ei) can be calculated as follows:
The effective interest rate is 6.09%.
Plan A cash flow is each year pays $1,000,000. Since the payment is made at the beginning of each year, the time period (n) is five. The present worth of plan A (PWA) can be calculated as follows:
The present worth of the plan A is -$5,202,092.
Plan B cash flow is each semiannual pays $600,000. Since the payment is made at the beginning of each semiannual for the first year, the time period (n1) is two, time period 2 (n2) is three, and time period 3 (n3) is seven. Since the interest is compounded semiannually, the semiannual interest (i1) is 3%
The present worth of plan B is -$4,681,215.6.
Plan C’s cash flow is $1,500,000 at the beginning of the year and pays $500,000 at the end of the second year. Thus, the time period (n1) is four, time period 2 (n2) is six, and time period 3 (n3) is 10. Since the interest is compounded semiannually, the semiannual interest (i1) is 3%
The present worth of plan C is -$3,555,159.85. Since the present worth of plan C is greater than other two plans, select plan C.
(b):
Spreadsheet function for calculating the present worth.
(b):

Explanation of Solution
The interest rate is filled in B2, cash flows are filled in B5 to B10. The spreadsheet function for plan A is given below:
=
The above function gives the value of -$5,202,070.
The interest rate is filled in D2, cash flows are filled in D5 to D15. The spreadsheet function for plan A is given below:
= NPV($D2,D6:D15)+D5
The above function gives the value of -$4,681,182.
The interest rate is filled in E2, and cash flows are filled in E5 to E15. The spreadsheet function for plan A is given below:
= NPV($E2,E6:E15)+E5
The above function gives the value of -$3,572,517.
Since the present worth of plan C is greater than other two plans, select plan C.
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Chapter 5 Solutions
ENGINEERING ECONOMY(LOOSELEAF)
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