Cost of Equity-CAP

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XYZ, Inc. has a beta of 0.8. The yield on a 3-month T-bill is 4%, and the yield on a 10-year T-bond is 6%. The market risk premium is 5.5%, and the return on an average stock in the market last year was 15%.

What is the estimated cost of common equity using the CAPM? Show your work.
Complete problems: NPV, IRR, MIRR, Profitability Index, Payback, Discounted Payback
A project has an initial cost of $60,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 12%. Show your work.

What is the project’s NPV? (Hint: Begin by constructing a timeline.)
What is the project’s IRR?
What is the project’s MIRR?
What is the project’s PI?
What is the project’s payback period?
What is the project’s discounted payback period?
Your division is considering two investment projects, each of which requires an up-front expenditure of 20 million. You estimate the investment will produce the following net cash flows:
Year Project A Project B

1 $5,000,000 $20,000,000

2 10,000,000 10,000,000

3 20,000,000 6,000,000

What are the two projects’ net present values, assuming the cost of capital is 5%? 10%? 15%?
What are the two projects’ IRRs at the same cost of capital? Show your work.

Sample Solution

Problem 1: Cost of Common Equity

Understanding the CAPM Model

The Capital Asset Pricing Model (CAPM) is used to determine the expected return on an investment based on its systematic risk. The formula for CAPM is:  

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Cost of Equity (Re) = Risk-free Rate (Rf) + Beta (β) * Market Risk Premium (MRP)

Given Values:

  • Beta (β) = 0.8
  • Risk-free Rate (Rf) = Yield on a 3-month T-bill = 4%
  • Market Risk Premium (MRP) = 5.5%

Calculation:

Re = 4% + 0.8 * 5.5%
  = 4% + 4.4%
  = 8.4%

Therefore, the estimated cost of common equity using the CAPM is 8.4%.

Problem 2: NPV, IRR, MIRR, Profitability Index, Payback, Discounted Payback

Given Values:

  • Initial Cost = $60,000
  • Annual Net Cash Inflows = $10,000
  • Number of Years = 8
  • Cost of Capital = 12%

NPV (Net Present Value)

NPV is the difference between the present value of cash inflows and the initial investment.

Timeline:

Year Cash Flow
0 -$60,000
1 $10,000
2 $10,000
3 $10,000
4 $10,000
5 $10,000
6 $10,000
7 $10,000
8 $10,000

Calculation:

NPV = Σ [Cash Flow / (1 + r)^t] - Initial Investment

Where:

  • r = discount rate (cost of capital)
  • t = time period

Using a financial calculator or spreadsheet, you can calculate the present value of each cash flow and sum them up. Then, subtract the initial investment.

NPV = [Result of calculations]

IRR (Internal Rate of Return)

IRR is the discount rate that makes the NPV of a project equal to zero.

This requires trial and error or using a financial calculator or spreadsheet function.

IRR = [Result of calculations]

MIRR (Modified Internal Rate of Return)

MIRR assumes that cash inflows are reinvested at the cost of capital.

MIRR = [Result of calculations]

Profitability Index (PI)

PI is the ratio of the present value of future cash flows to the initial investment.

PI = Present Value of Future Cash Flows / Initial Investment  
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PI = [Result of calculations]

Payback Period

Payback period is the length of time required to recover the initial investment.

Payback Period = Initial Investment / Annual  
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 Net Cash Inflow

Payback Period = [Result of calculations]

Discounted Payback Period

Discounted payback period is the length of time required to recover the initial investment, considering the time value of money.

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