Question

Last Tuesday, Cute Camel Woodcraft Company lost a portion of its planning and financial data when its server and it backup server crashed. The company's CFO remembers that the internal rate of return (IRR) of Project Lambda is 13.2%, but he can't recall how much Cute Camel 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 Lambda. They are: 

The CFO has asked you to compute Project Lambda s initial investment using the information currently available 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 flows are discounted using the project's IRR. 

• The level of risk exhibited by Project Lambda is the same as that exhibited by the company's average project, which means that Project Lambda's net cash flows can be discounted using Cute Camel's 8% desired rate of return. 

Given the data and hints, Project Lambda's initial investment is_______ , and its NPV is_______ (rounded to the nearest whole dollar).

Answer 1

NPV of a project is zero at IRR. Thus, it can be said that the present value of the cash flows (from year 1 to year 4 ) at IRR (13.2\%) is equal to the initial investment.

Hence, the initial investment of the project can be calculated by discounting the cash flows (from year 1 to year 4) at IRR (13.2\%).

Calculate the initial investment using the following formula:

$$ \text { Present value }=\frac{\mathrm{CF}_{1}}{(1+\mathrm{r})^{1}}+\frac{\mathrm{CF}_{2}}{(1+\mathrm{r})^{2}}+\frac{\mathrm{CF}_{3}}{(1+\mathrm{r})^{3}}+\frac{\mathrm{CF}_{4}}{(1+\mathrm{r})^{4}} $$

Here, CF stands for cash flow and \(r\) stands for discount rate.

Substitute the values in the formula.

$$ \begin{aligned} \text { Present value } &=\frac{\mathrm{CF}_{1}}{(1+\mathrm{r})^{1}}+\frac{\mathrm{CF}_{2}}{(1+\mathrm{r})^{2}}+\frac{\mathrm{CF}_{3}}{(1+\mathrm{r})^{3}}+\frac{\mathrm{CF}_{4}}{(1+\mathrm{r})^{4}} \\ &=\frac{\$ 2,400,000}{(1+0.132)^{1}}+\frac{\$ 4,500,000}{(1+0.132)^{2}}+\frac{\$ 4,500,000}{(1+0.132)^{3}}+\frac{\$ 4,500,000}{(1+0.132)^{4}} \\ &=\$ 11,474,565 \end{aligned} $$

Therefore, the initial investment of the project is \(\$ 11,474,565\).

Calculate the NPV of the as follows:

$$ \begin{aligned} \mathrm{NPV} &=\mathrm{CF}_{0}+\frac{\mathrm{CF}_{1}}{(1+\mathrm{r})^{1}}+\frac{\mathrm{CF}_{2}}{(1+\mathrm{r})^{2}}+\frac{\mathrm{CF}_{3}}{(1+\mathrm{r})^{3}}+\frac{\mathrm{CF}_{4}}{(1+\mathrm{r})^{4}} \\ &=-\$ 11,474,565+\frac{\$ 2,400,000}{(1+0.08)^{1}}+\frac{\$ 4,500,000}{(1+0.08)^{2}}+\frac{\$ 4,500,000}{(1+0.08)^{3}}+\frac{\$ 4,500,000}{(1+0.08)^{4}} \\ &=\$ 1,485,561 \end{aligned} $$

Therefore, the NPV of the project is \(\$ 1,485,561\).