The iniital investment is $1,500. NPC has the opportunity to invest in a project
ID: 2766853 • Letter: T
Question
The iniital investment is $1,500. NPC has the opportunity to invest in a project that has a 75% chance of generating $500 per year for 7-years under good conditions or a 25% chance of generating $25 per year for 7-years. Assuming that all cash flows are discounted at 10%, calculate the effect of waiting on the project's risk, using the same data. By how much will delaying reduce the project's coefficient of variation? (Hint: Use the expected NPV.)
a) 2.23 b) 2.46 c) 2.70 d) 2.97 e) 3.27
Please show your work so i can input on excel
Explanation / Answer
Calculation of NPV under good condition
Year
Cash flow
PVAF @10%
Discounted cash flow
0
(1,500.00)
1
(1,500.00)
1 to 7
500.00
4.8684
2,434.20
NPV
934.20
Calculation of NPV under bad condition
Year
Cash flow
PVAF @10%
Discounted cash flow
0
(1,500.00)
1
(1,500.00)
1 to 7
25.00
4.8684
121.71
NPV
(1,378.29)
NPV = 0.75 * 934.2 + 0.25*(1378.3)
NPV = 700.08 - 344.5
NPV = $356.08
The CV = SD/Expected NPV.
Invest immediately:
Probability
NPV
NPVi - E(NPV)
Squared Deviation
Squared deviation times probability
0.75
934.21
578.00
334,228.00
250,671.00
0.25
(1,378.29)
(1,734.00)
3,008,054.00
752,013.00
1
365.08
Variance
1,002,685.00
Standard deviation
1,001.34
Coefficient of variance
2.81
Delay, then invest in period 1 if the outlook is good:
Probability
NPV
NPVi - E(NPV)
Squared Deviation
Squared deviation times probability
0.75
616.03
154.00
23,718.00
17,789.00
0.25
-
(462.00)
213,463.00
53,366.00
1
462.02
Variance
71,154.00
Standard deviation
266.75
Coefficient of variance
0.58
Reduction in the CV due to waiting 2.23
Note that the problem implicitly assumes that the project is riskless if it is delayed. This is, of course, unrealistic. Note also that a lower cost of capital should be used to find the NPV of the “Go Now” deci- sion than the “Wait” decision. The appropriate cost of capital is often lowered by the existence of real options.
Calculation of NPV under good condition
Year
Cash flow
PVAF @10%
Discounted cash flow
0
(1,500.00)
1
(1,500.00)
1 to 7
500.00
4.8684
2,434.20
NPV
934.20
Calculation of NPV under bad condition
Year
Cash flow
PVAF @10%
Discounted cash flow
0
(1,500.00)
1
(1,500.00)
1 to 7
25.00
4.8684
121.71
NPV
(1,378.29)
NPV = 0.75 * 934.2 + 0.25*(1378.3)
NPV = 700.08 - 344.5
NPV = $356.08
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