8. The cash flow distribution associated with a five-year project is shown below
ID: 1126030 • Letter: 8
Question
8. The cash flow distribution associated with a five-year project is shown below. Time (years) 0 Cash flow ($) 10,000 4,000 4 5,500 5 6,100 4,400 5,000 Assuming that the cash flows are given in that year's $ and that a general monetary inflation rate of 5% applies throughout the project's life, determine the net present value using a minimal acceptable rate of return of 12%. [$10,403] Assuming that the cash flows are given in that year's $ and that a general monetary inflation rate of 6.25% applies throughout the project's life, determine the net present value using a minimal acceptable rate of return of 12%. [SI 1,165] a. b.Explanation / Answer
8. First we need to find the real interest rate. Formula:
1+ i = (1 + r)(1 + )
[Where ‘i’ is nominal interest rate, ‘r’ is real interest rate, and ‘’ is inflation rate]
1+0.12 = (1+r)(1+0.05)
1+r = 1.12/1.05 = 1.0666
r = 1.0666 – 1 = 0.0666
Real interest rate = 6.66% 1.0666, 1.1376, 1.2134, 1.29422, 1.3804.
• a. Net present value = -$10,000 + 4,000/(1.0666) + 4,400/(1.0666)^2 + 5,000(1.0666)^3 + 5,500(1.0666)^4 + 6,100/(1.0666)^5
Net present value = -$10,000 + 3,750.23 + 3,867.79 + 4,120.65 + 4,249.72 + 4,419.00
Net present value = -$10,000 + 20,407.39 = $10,407.39
Net present value = $10,407.
• Real interest rate:
1.12 = (1+r)(1.0625)
1+r = 1.12/1.0625 = 1.0541
r = 1.0541 – 1 = 0.0541
Real interest rate = 5.41%
Net present value = -$10,000 + 4,000/1.0541 + 4,400/1.1111 + 5,000/1.1712 + 5,500/1.2346 + 6,100/1.3013
Net present value = -$10,000 + 3,794.70 + 3,960.03 + 4,269.12 + 4,454.88 + 4,687.62
Net present value = -$10,000 + 21,166.35
Net present value = $11,166.
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