Question

Last Tuesday, Fuzzy Button Clothing Company lost a portion of its planning and finacial data when its server and its backup server crashed. The company's CFO remembers that the internal rate of return (IRR) of Project Delta is 14.6%, but he can't recall how much Fuzzy Button originally invested in the project nor the project's net present value (NPV). However, he found a note that contained the annual net cash flows expected to be generated by Project Delta. They are:

Year	Cash Flow
Year 1	$1,600,000
Year 2	$3,000,000
Year 3	$3,000,000
Year 4	$3,000,000

The CFO has asked you to compute project Delta's initial investment using the information currently avaliable to you. He has offered the following suggestions and observations:

A project's IRR represents the return the project would generate when its NPV is zero or the discounted value of its cash inflows equals the discounted value of its cash outflows - when the cash outflows are discounted using the project's IRR.

The level of risk exhibited by Project Delta is the same as that exhibit by the company's average project, which means that Project Delta's net cash flows can be discounted using Fuzzy Button's 9% WACC.

Given the data and hints, Project Delta's initial investment is ____________ (a. $7,746,571, b. $8,634,704, c. $7,413,064, d. $7,524,980) and its NPV is _____________(a. $919,523, b. $1,226,030, c. $1,021,692, d. $868,438) (rounded to the nearest whole dollar)

A projects IRR will __________ (a. increase, b. decrease, c. stay the same) if the project's cash inflows decrease, and everything else is unaffected.

Answer 1

Initial investment can be calculated by discounting the cash flows at IRR.

Calculate the initial investment as follows:

$$ \begin{aligned} \mathrm{PV} &=\frac{\mathrm{CF}_{1}}{(1+\mathrm{r})^{1}}+\frac{\mathrm{CF}_{2}}{(1+\mathrm{r})^{2}}+\frac{\mathrm{CF}_{3}}{(1+\mathrm{r})^{3}}+\frac{\mathrm{CF}_{4}}{(1+\mathrm{r})^{4}} \\ &=\left[\frac{\$ 1,600,000}{(1+0.146)^{1}}+\frac{\$ 3,000,000}{(1+0.146)^{2}}+\frac{\$ 3,000,000}{(1+0.146)^{3}}+\frac{\$ 3,000,000}{(1+0.146)^{4}}\right] \end{aligned} $$

\(=\$ 7,413,063.6911\) (or) \(\$ 7,413,064\) (After rounding to nearest dollar)

Note: Here PV stands for present value and CF stands for cash flows.

Therefore, the correct answer is option (c).

Calculate the NPV at WACC:

$$ \begin{aligned} \mathrm{NPV} &=\mathrm{CF}_{0}+\frac{\mathrm{CF}_{1}}{(1+\mathrm{r})^{1}}+\frac{\mathrm{CF}_{2}}{(1+\mathrm{r})^{2}}+\frac{\mathrm{CF}_{3}}{(1+\mathrm{r})^{3}}+\frac{\mathrm{CF}_{4}}{(1+\mathrm{r})^{4}} \\ &=\left[-\$ 7,413,064+\frac{\$ 1,600,000}{(1+0.09)^{1}}+\frac{\$ 3,000,000}{(1+0.09)^{2}}+\frac{\$ 3,000,000}{(1+0.09)^{3}}+\frac{\$ 3,000,000}{(1+0.09)^{4}}\right] \end{aligned} $$

\(=\$ 1,021,691.9614(\) or \() \$ 1,021,692\) (After rounding to nearest dollar)

Therefore, the correct answer is option (c).

If the cash inflows are higher, the IRR of the project will also be higher. Decrease in inflows leads to decrease in IRR.

Therefore, the correct answer is option (b).