Question

A project requires an investment of $20,000 and will return $26,500 after one year. Suppose the 10-year Treasury bill rate is 5%, and the project has a risk premium of 12%.

A) Should this project be taken? Also Calculate the IRR of this project.

B)If the manager wants to finance the project solely with equity, what is the equity holder’s valuation of this project?

C)If the manager wants to finance the project 50% with equity and 50% with 10-year T-bill, what is equity holder’s valuation of this project?

D)Explain in your own words why the equity holder’s valuation of the project differs between B) and C).

E)Using the information of this project, draw a graph illustrating the relation between cost of levered equity and the leverage ratio [D/ (D+E)]

Please Help!

Answer 1

Since you have asked a question with multiple sub parts, i will address first four of them.

All the financials below are in $.

C₀ = 20,000; C₁ = 26,500

Discount rate, R = 10-year Treasury bill rate + project risk premium = 5% + 12% = 17%

Part (a)

NPV = -C₀ + C₁ / (1 + R) = -20,000 + 26,500 / (1 + 17%) =  2,649.57. Since NPV is positive, this project should be taken.

When discount rate is equal to IRR, then NPV of the project is zero.

Hence, -C₀ + C₁ / (1 + IRR) = -20,000 + 26,500 / (1 + IRR) = 0

Hence, IRR = 26,500 / 20,000 - 1 = 32.50%

Part (b)

Since the project is financed solely with equity, the equity holder's valuation of the project = C₁ / (1 + R) = 26,500 / (1 + 17%) =  22,649.57

Part (c)

Discount rate, WACC = 50% x t bill rate + 50% x cost of equity = 50% x 5% + 50% x 17% = 11%

Hence, value of the project = C₁ / (1 + WACC) = 26,500 / (1 + 11%) =  23,873.87

Hence, value of the equity holders = Total value - value of debt =  23,873.87 - 50% x 20,000 =  13,873.87

Part (d)

Equity holders valuation of the project differs because of different discount rates used to discount the future cash flow. In case of leverage (i.e. debt funding), the overall value of the project improves because cost of debt is lower than cost of equity thereby lowering the overall WACC.