Quiz 3Midwest manufacturing Company is considering two mutually exclusive investments. The projects’ expected cash flow as follows.

a) Construct NPV (net present value) if the cost of capital is 10 percent.

b) Construct NPV (net present value) if the cost of capital is 17 percent.

c) If you were told that each project’s cost is 10 percent, which project should be selected? If the cost of capital were 17 percent, what would proper choice be?

Answer

a) Construct NPV (net present value) if the cost of capital is 10 percent.

Answer

b) Construct NPV (net present value) if the cost of capital is 17 percent.

Answerc) If you were told that each project’s cost is 10 percent, which project should be selected? If the cost of capital were 17 percent, what would proper choice be?

10%Project A : $7,918.75Project B : - $ 405

17%Project A : $2,018.75Project B : - $ 405

We would select Project A because the amount is more than 0

We would select Project A because the amount is more than 0

Chapter 11: Capital BudgetRisk-Adjusted Discount Rates

A method for incorporating the project’s level of risk into the capital-budgeting process, in which the discount rate is adjusted upward to compensate for higher than normal risk or downward to adjust for lower than normal risk.

𝑁𝑃𝑉=∑𝑡=1

𝑛 𝐹𝐶𝐹 𝑡

(1+𝑘¿¿∗)𝑡− 𝐼𝑂¿

FCF = the annual expected free cash flow in time period t.IO = the initial cash outlay.K* = the risk-adjusted discount rate.N = the project’s expected life.

Example 1A toy manufacture is considering the introduction of a line of fishing equipment with an expected life of five years. In the past, this firm has been quite conservative in its investment in new products, sticking primarily to standard toys. In this context, the introduction of a line of fishing equipment is considered an abnormally risky project. Management thinks that the normal required rate of return for the firm of 10 percent is not sufficient. Instead, the minimally acceptable rate of return on this project should be 15 percent. The initial outlay would be $110,000, and the expected free cash flows from this project are as given below:

Example 1

𝑁𝑃𝑉=∑𝑡=1

5 $ 30,000(1+0.15)5

−$ 110,000𝑁𝑃𝑉=∑𝑡=1

5 $30,000(1+0.10)5

−$110,000

The project would have been accepted Project B with a net present value $3,700

Example 2Bennett Company wishes to apply the Risk-Adjusted Discount Rate (RADR) approach to determine whether to implement Project A or B.

rate of return on Project A : 14%Project B : 11%

Example 2

𝑁𝑃𝑉=∑𝑡=1

5 $ 14,000(1+0.14 )5

−$ 42,000 𝑁𝑃𝑉=∑𝑡=1

5 $10 ,000(1+0.11)5

−$4 5 ,000

The project would have been accepted Project B with a net present value $9,802

Certainty Equivalent vs. Risk-Adjusted Discount Rate Methods

Certainty EquivalentStep 1 : Adjust the free cash flows, ,

downward for risk by multiplying them corresponding certainly equivalent coefficient,

Step 2 : Discount the certainty equivalent riskless cash flows back to the present using the risk-free rate of interest.

Step 3 : Apply the normal decision criteria, except in the case of internal rate of return, where the risk-free rate of interest replaces the required rate of return as the hurdle rate.

Risk-Adjusted Discount RateStep 1 : Adjust the discount rate

upward for risk, or down in the case of less than normal risk.

Step 2 : Discount the expected free cash flows back to the present using the risk-adjusted discount rate.

Step 3 : Apply the normal decision criteria except in the case of the internal rate of return, where the risk-adjusted discount rate replaces the required rate of return as the hurdle rate

Certainty Equivalent ExampleA firm with a 10 percent required rate of return is considering building new research facilities with an expected life of five years. The initial outlay associated with this project involves a certain cash outflow of $120,000. The expected cash inflows and certainty equivalent coefficients, , are as follows:

The risk-risk free rate of interest is 6 percent. What is the project’s net present value?

Answer

Comparing Certainty Equivalent and Risk Adjusted Discount Rate Methods

A firm with a required rate of return of 10 percent is considering introducing a new product. This product has an initial outlay of $800,000, and expected life of 10 years, and free cash flows of $10 0,000 each year during its life. Because of the increased risk associated with this project, management is requiring a 15 percent rate of return.

Comparing Certainty Equivalent and Risk Adjusted Discount Rate Methods

Certainty Equivalent

Comparing Certainty Equivalent and Risk Adjusted Discount Rate Methods

Risk-Adjusted Discount Rate Method