In financial analysis, it is important to select an appropriate discount rate. A
ID: 2656136 • Letter: I
Question
In financial analysis, it is important to select an appropriate discount rate. A project's discount rate must be high to compensate investors for the project's risk. The return that shareholders require from the company as a compensation for their investment risk is referred to as the cost of equity Consider this case: Sunny Co. is a 100% equity-financed company (no debt or preferred stock); hence, its WACC equals its cost of common equity. Sunny Co.'s retained earnings will be sufficient to fund its capital budget in the foreseeable future. The company has a beta of 1.50, the risk-free rate is 5.0%, and the market return is 6.5%. What is Sunny Co.'s cost of equity? ? 16.25% 24.13% 8.75% ? 7.25%Explanation / Answer
- According to CAPM,
Cost of equity = Risk free rate + beta*(Market return - risk free rate)
= 5% + 1.5*(6.5%-5%) = 7.25%
- Projects W,Y,Z are to be expected.
Required capital = 6875+3595+4955 = $15425
- If the crossover rate on the NPV profile is below the horizontal axis, the methods will always agree.
NPV is calculated by discounting the cashflows
PV = C/(1+r)^n
C - Cashflow
r - Discount rate
n - years to the cashflow
Project X:
NPV = -1500 + 200/(1+0.14)^1 + 400/(1+0.14)^2 + 600/(1+0.14)^3 + 1000/(1+0.14)^4 = -$19.71
IRR is the rate at which NPV = 0
0 = -1500 + 200/(1+IRR)^1 + 400/(1+IRR)^2 + 600/(1+IRR)^3 + 1000/(1+IRR)^4
By trail and error, IRR = 13.49%
Project Y:
NPV = -1500 + 900/(1+0.14)^1 + 600/(1+0.14)^2 + 300/(1+0.14)^3 + 200/(1+0.14)^4 = $72.06
IRR is the rate at which NPV = 0
0 = -1500 + 900/(1+IRR)^1 + 600/(1+IRR)^2 + 300/(1+IRR)^3 + 200/(1+IRR)^4
By trail and error, IRR = 17.07%
Using both NPV and IRR projects, only project Y should be selected.
So, the methods will agree.
- The NPV calculation implicitly assumes that intermediate cash flows are reinvested at the Cost of capital, and the IRR calculation assumes that the rate at which cash flows can be reinvested is the internal rate of return.
- As a result, when evaluating mutually exclusive projects, the NPV method is usually the better decision criterion.