MGMT E-2900B

PROBLEM SOLVING SESSION

FEBRUARY 2, 2010

CAPITAL BUDGETING

Use the following data to answer the following 5 questions

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

1.) What is the project's payback period?

A. 1.5 yearsB. 2.0 yearsC. 2.5 years

Year 1 - $4,500 - $7,500 = -$3,000Year 2 - $3,000 - $3,000 = $0Year 3 - $3,000

1.) What is the project's payback period?

A. 1.5 yearsB. 2.0 yearsC. 2.5 years

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

2.) The project's discounted payback period is closest to:

A. 1.4 yearsB. 2.0 yearsC. 2.5 years

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500/1.10 = $4,090.91 - $7,500 = -$3,409.09

Year 2 - $3,000/1.102 = $2,479.34 - $3,409.09 = -$929.75

Year 3 - $3,000/1.103 = $2,253.94 - $929.75 = $$1,324.19

2.) The project's discounted payback period is closest to:

A. 1.4 yearsB. 2.0 yearsC. 2.5 years

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

3.) What is the project's NPV?

A. -$309B. +$883C. +$1,324

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

NPV = -$7,500 + $4,500/1.10 + $3,000/1.102 + $3,000/1.103

NPV = -$7,500 + $4,090.91 + $2,479.34 + $2,253.94

3.) What is the project's NPV?

A. -$309B. +$883C. +$1,324

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

4.) The project's IRR is closest to:

A. 10%B. 15%C. 20%

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

Using Excel spreadsheet=IRR(values, guess)values are the cash flowsguess is your estimate of IRR (a starting point to calculate)20.64%

4.) The project's IRR is closest to:

A. 10%B. 15%C. 20%

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

5.) What is the project's profitability index?

A. 0.72B. 1.18C. 1.72

A company is considering the purchase of a copier that costs $7,500.Assume a required rate of return of 10% and the followingcash flow schedule:

Year 1 - $4,500Year 2 - $3,000Year 3 - $3,000

Profitability Index (PI) = PV of future cash flows/CF0

Cash flows = $4,090.91 + $2,479.34 + $2,253.94 = $8,824.19PI = $8,824.19/$7,500

5.) What is the project's profitability index?

A. 0.72B. 1.18C. 1.72

Use the following data for the next 3 questions

An analyst has gathered the following data about two projects,each with a 12% required rate of return.

Project A Project B

Initial Cost $30,000 $40,000

Life 5 years 4 years

Cash Inflows $10,000/year 15,000/year

1.) If the projects are independent, the company should:

A. Accept Project A and reject Project BB. Reject Project A and accept Project BC. Accept both projects

2.) If the projects are mutually exclusive, the company should:

A. Reject both projectsB. Accept Project A and reject Project BC. Reject Project A and accept Project B

3.) The NPV profiles of two projects will intersect:

A. At their internal rates of returnB. If they have different discount ratesC. At the discount rate that makes their net present values equal

Project A

Initial Cost = $30,000 = PVLife = 5 years = nCash Inflows = $10,000/year = PMTRequired rate of return = 12% = i

Using Excel, the formula is

=NPV(rate,value1,value2,value3,value4,value5) - PVwhere the rate is the required rate of returnvalue1 … value5 represents the cash flowscash outflow is entered as a negative valuecash inflow is entered as a positive value

Net Present Value = $6,047.76

Project B

Initial Cost = $40,000 = PVLife = 4 years = nCash Inflows = $15,000/year = PMTRequired rate of return = 12% = i

Using Excel, the formula is

=NPV(rate,value1,value2,value3,value4) - PVwhere the rate is the required rate of returnvalue1 … value4 represents the cash flowscash outflow is entered as a negative valuecash inflow is entered as a positive value

Net Present Value = $5,560.24

1.) If the projects are independent, the company should:

A. Accept Project A and reject Project BB. Reject Project A and accept Project BC. Accept both projects

2.) If the projects are mutually exclusive, the company should:

A. Reject both projectsB. Accept Project A and reject Project BC. Reject Project A and accept Project B

3.) The NPV profiles of two projects will intersect:

A. At their internal rates of returnB. If they have different discount ratesC. At the discount rate that makes their net present values equal

The net present value method is a better method of evaluation than the internal rate of return method because the NPV method A. assumes cash flows are reinvested at the internal rate of return.B. is a more liberal method of analysis.C. assumes that cash flows can be reinvested at the firm's more conservative cost of capital.

The net present value method is a better method of evaluation than the internal rate of return method because the NPV method A. assumes cash flows are reinvested at the internal rate of return.B. is a more liberal method of analysis.C. assumes that cash flows can be reinvested at the firm's more conservative cost of capital.

a.b.c.

d.

Project S.Project L.Both projects are equally sensitive to changes in the WACC since their NPVs are equal at all costs of capital.

Neither project is sensitive to changes in the discount rate, since both have NPV profiles that are horizontal.

Projects S and L both have an initial cost of $10,000, followed by a series of positive cash inflows. Project S’s undiscounted net cash flows total to $20,000, while L’s total undiscounted flows are $30,000. At a WACC of 10%, the two projects have identical NPVs. Which project’s NPV is more sensitive to changes in the WACC?

NPV Profiles

This question can be addressed by creating a graphical expression of the two cash flows

We know that at a WACC of 10% the NPV’s are identical

We know that Project S has an undiscounted cash flow of $20,000 (the same as saying that the WACC is 0%), and we know that Project L has an undiscounted cash flow of $30,000

We can use this information to plot points on a graph to answer the question

a.b.c.

d.

Project S.Project L.Both projects are equally sensitive to changes in the WACC since their NPVs are equal at all costs of capital.

Neither project is sensitive to changes in the discount rate, since both have NPV profiles that are horizontal.

Projects S and L both have an initial cost of $10,000, followed by a series of positive cash inflows. Project S’s undiscounted net cash flows total to $20,000, while L’s total undiscounted flows are $30,000. At a WACC of 10%, the two projects have identical NPVs. Which project’s NPV is more sensitive to changes in the WACC?

Westchester Corp. is considering two equally risky, mutually exclusive projects, both of which projects have normal

have the same NPV. Given this information,, which of the following statements is CORRECT?

a. If the WACC is 13%, Project A's NPV will be higher than Project B's.b. If the WACC is 9%, Project A's NPV will be higher than Project B's.c. If the WACC is 6%, Project B's NPV will be higher than Project A's.d. If the WACC is greater than 14%, Project A's IRR will exceed Project B's.e. If the WACC is 9%, Project B's NPV will be higher than Project A's.

cash flows. Project A has an IRR of 11%, while Project B's IRR is 14%. When the WACC is 8%, the projects

NPV Profiles

Again, this problem can be addressed graphically

IRR is the point on the graph where NPV = 0

We know the IRR’s for each project and we know the WACC where the NPV’s are equal

Westchester Corp. is considering two equally risky, mutually exclusive projects, both of which projects have normal

have the same NPV. Given this information,, which of the following statements is CORRECT?

a. If the WACC is 13%, Project A's NPV will be higher than Project B's.b. If the WACC is 9%, Project A's NPV will be higher than Project B's.c. If the WACC is 6%, Project B's NPV will be higher than Project A's.d. If the WACC is greater than 14%, Project A's IRR will exceed Project B's.e. If the WACC is 9%, Project B's NPV will be higher than Project A's.

cash flows. Project A has an IRR of 11%, while Project B's IRR is 14%. When the WACC is 8%, the projects

COST OF CAPITAL

After Tax Cost of Debt

A company has $8 million in debt outstanding with a coupon rate of 10%. Currently, the yield to maturity (YTM) is 12%. If the firm’s tax rate is 35%, what is the company’s after-tax cost of debt?

a. 6.5%

b. 7.8%

c. 12.0%

After-Tax Cost of Debt

The primary question is which cost to use, the coupon rate or the yield to maturity (YTM).

The argument for coupon rate is that is the current cash outflow for the company debt

The argument for yield to maturity is that it represents the rate at which a firm can issue new debt. The yield to maturity is the stronger argument because it reflects current market and current firm conditions

The after-tax cost of debt is kd(1 – t) where t = tax rate

After-Tax Cost of Debt

A company has $8 million in debt outstanding with a coupon rate of 10%. Currently, the yield to maturity (YTM) is 12%. If the firm’s tax rate is 35%, what is the company’s after-tax cost of debt?

a. 6.5%

b. 7.8%

c. 12.0%

Marginal Cost of Capital

A company is planning a $20 million expansion. The expansion is to be financed by selling $8 million in new debt and $12 million in new common stock. The before-tax required return on debt is 10% and 15% for equity. If the company is in the 30% tax bracket, the company’s marginal cost of capital is closest to:

a. 13.0%b. 8.2%c. 11.8%

Marginal Cost of Capital

This problem requires the calculation of the cost of capital of the new financing

The equation is the same as for the cost of capital = (wd x kd(1-t)) + (we x ke)

Wd = 40% ($8 million/$20 million)

Kd = 10%(1 – 30%) = 7%

We = 60% ($12 million/$20 million)

Ke = 15%

Marginal Cost of Capital

A company is planning a $20 million expansion. The expansion is to be financed by selling $8 million in new debt and $12 million in new common stock. The before-tax required return on debt is 10% and 15% for equity. If the company is in the 30% tax bracket, the company’s marginal cost of capital is closest to:

a. 13.0%b. 8.2%c. 11.8%