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:  

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:

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   

PI = [Result of calculations]

Payback Period

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

Payback Period = Initial Investment / Annual   

 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.