Question

Consider a project with free cash flows in one year of ​$145,769 or $167,218 with each outcome being equally likely. The initial investment required for the project is ​$108, 996 and the​project'scost of capital is 22 %.The​risk-freeinterest rate is 7 %

.a. What is the NPV of this​project?

b. Suppose that to raise the funds for the initial​investment,the project is sold to investors as an​all-equityfirm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this

waylong dashthat ​is,what is the initial market value of the unlevered​equity?  

c.Suppose the initial ​$108,996 is instead raised by borrowing at the​risk-freeinterest rate. What are the cash flows of the levered​equity,what is its initial value and what is the initial equity according to​MM?

Answer 1

a) NPV of Project

NPV = Discounted Cashflows - Initial Investment

Discounted Cashflows = Future probable cashflows discounted at the cost of capital

Initial Investment = Amount needed initially to start the project

Calculating the Discounting factor

First understand that Discounting rate i.e. The cost of Capital

Discounting factor for year 1 = 1/(1 + Discounting rate)

Discounting factor for year 2  = 1/(1 + Discounting rate)²

Discounting factor for year 3 = 1/(1 +Discounting rate)³

^{and so on.}

We here in this question just need he discounting factor for just the first year

Therefore, Discounting rate = cost of capital = 22% or 0.22

Discounting factor = 1/Discounting rate = 1/(1 + 0.22) =1/1.22 = 0.8196

Now, the discounted cashflows for the first year can be either $145,769 or $167,218, with equal probability.

equal probability = 0.5 for each

Hence, the expected cashflow for the first year is-

$145,769 * 0.5 + 0.5 * $167,218 = 72884.5 + 83609 = $156,493.5

The discounted expected cash flow for year 1 = expected cashflow for the first year * Discounting factor for first year

= 156493.5 * 0.8196

= $128,215.125

Now, NPV = Discounted Cashflows - Initial Investment

= $128,215.125 - $108, 996

= $19,219.125

b)

As the project shall be given all equity for initial investment the value of the project shall be equal to the value of funds i.e. cash flow that the investor can get after 1 year from this project. From the above calculation we get that the value of cashflows expected to occur after first year is $128,215.125, that is the expected discounted cash flows.

hence the value of project un-levered = $128,215.125

c)

The project is levied now. Which means that a debt has been taken to find the project. hence we need to pay interest for the debt raised.

Which implies that the future cash flows shall be reduced by the amount of interest payments.

The expected cashflows as per calculation in answer a) is $156,493.5

The Interest on debt is to be calculated at risk free rate that is 7%

Initial Investment = $108,996

Interest thereon = $108,996 * 7% = 7629.72

The expected cashflows reduced by interest amount = $156,493.5 - 7629.72 = 148,863.78

Answers-

1. ) Cashflows for levered equity = $148,863.78

2.) Initial Value of project

As we obtain the initial investment as debt. we need to pay back that amount after 1 year.

debt amount * Discounting factor for first year

Thus, discounted amount of debt to be paid after 1 year = $108,996 * 0.8196

= 89,333.12

Initial Value of project = Cashflows for levered equity - Discounted Initial Investment

= 148,863.78 - 89,333.12

= $59,530.659