Question
In: Finance
(NPV with varying required rates of return) Gubanich Sportswear is considering building a new factory to...
(NPV with varying required rates of return) Gubanich Sportswear is considering building a new factory to produce aluminum baseball bats. This project would require an initial cash outlay of $4,000,000 and would generate annual free cash inflows of $1,000,000 per year for 7 years. Calculate the project's NPV given:
a. A required rate of return of 9 percent
b. A required rate of return of 11 percent
c. A required rate of return of 15 percent
d. A required rate of return of 16 percent
Solutions
Expert Solution
NPV = 
Rt / ( 1 +
i)t , t varies from 1 to n
where
Rt = Cash flow netted (Inflow - Outflow) during the period "t"
i = Discount rate
t = number of periods
Hence, we can use the above formula to construct following table:
| Case A | ||||||||
| Discount Rate (r) | 9% | |||||||
| years | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Cash-Outflows | 40,00,000 | |||||||
| Cash-Inflows | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | |
| Net Cashflows (Inflow - Outflow) | -40,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 |
|
Discounted Cashflow = Net CF / (1+r)^years |
-40,00,000 | 9,17,431 | 8,41,680 | 7,72,183 | 7,08,425 | 6,49,931 | 5,96,267 | 5,47,034 |
| NPV = sum of all discounted CF | 10,32,953 |
| Case B | ||||||||
| Discount Rate (r) | 11% | |||||||
| years | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Cash-Outflows | 40,00,000 | |||||||
| Cash-Inflows | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | |
| Net Cashflows (Inflow - Outflow) | -40,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 |
|
Discounted Cashflow = Net CF / (1+r)^years |
-40,00,000 | 9,00,901 | 8,11,622 | 7,31,191 | 6,58,731 | 5,93,451 | 5,34,641 | 4,81,658 |
| NPV = sum of all discounted CF | 7,12,196 |
| Case C |
| Discount Rate (r) | 15% | |||||||
| years | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Cash-Outflows | 40,00,000 | |||||||
| Cash-Inflows | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | |
| Net Cashflows (Inflow - Outflow) | -40,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 |
|
Discounted Cashflow = Net CF / (1+r)^years |
-40,00,000 | 8,69,565 | 7,56,144 | 6,57,516 | 5,71,753 | 4,97,177 | 4,32,328 | 3,75,937 |
| NPV = sum of all discounted CF | 1,60,420 |
| Case D | ||||||||
| Discount Rate (r) | 16% | |||||||
| years | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Cash-Outflows | 40,00,000 | |||||||
| Cash-Inflows | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | |
| Net Cashflows (Inflow - Outflow) | -40,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 | 10,00,000 |
|
Discounted Cashflow = Net CF / (1+r)^years |
-40,00,000 | 8,62,069 | 7,43,163 | 6,40,658 | 5,52,291 | 4,76,113 | 4,10,442 | 3,53,830 |
| NPV = sum of all discounted CF | 38,565 |
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