Degnan Dance Company, Inc

BA 340

Final review questions’ solutions

1. Degnan Dance Company, Inc., a manufacturer of dance and exercise apparel, is considering replacing an existing piece of equipment with a more sophisticated machine. The following information is given.

Existing Machine Proposed Machine

______

Cost = $100,000 Cost = $150,000

Purchased 2 years ago Installation = $20,000

Depreciation using MACRS over Depreciationthe MACRS

a 5year recover schedule 5year recovery schedule will be used.

Current market value = $105,000

Five year usable life remaining Five year usable life expected

Earnings Before Depreciation and Taxes

Existing Machine Proposed Machine

______

Year 1 $160,000 Year 1 $170,000

2 150,000 2 170,000

3 140,000 3 170,000

4 140,000 4 170,000

5 140,000 5 170,000

The proposed machine would be sold at book value at the end of the fifth year. The existing machine would be discarded after its remaining useful life if it was maintained. No working capital investment is required. The firm’s cost of capital is 10% and its tax rate is 40%. Should the new machine be purchased?

Solution:Since we are evaluating just one project, we can use NPV.

The required rate of return is 10%

Incremental cash flows:

Proposed machine:

Initial cash flows: Purchase price + installation = $170,000

Operating cash flows:

Using a 5-yr MACRS schedule, depreciation for the proposed machine for 5 years is:

Yr. 1: 170000 * 0.2= 34000

2:170000 * 0.32= 54400

3: 32640

4: 19580

5: 19580

OCFs:Yr12345

EBDepr170000170000170000170000170000

- Depr3400054400326401958019580

EBIT136000115600137360150420150420

-taxes5440046240549486016860168

+Depr3400054400326401958019580

OCF115600123760115052109832109832

Terminal cash flow:

Sale of proposed machine (at book value):

Book value = 170000 – 34000 – 54400 – 32640 – 19580 – 19580 = 9800

Existing machine:

Sale of existing machine (included in initial cash flows):

Book value = 100000 – (100000 * 0.2) – (100000 * 0.32) = 48000

Cash flow from sale: 105000 – (105000 – 48000) * 0.4 = 82200

Operating cash flows lost:

The existing machine is to be used for 5 more years:

Depreciation:

Yr. 1: 100000 * 0.192= 19200

2:100000 * 0.1152= 11520

3:100000 * 0.1152 = 11520

4:100000 * 0.0576 = 5760

5:0

OCFs:Yr12345

EBDepr160000150000140000140000140000

- Depr19200115201152057600

EBIT140800138480128480134240140000

-taxes5632055392513925369656000

+Depr19200115201152057600

OCF10368094608886088630484000

NPV:

(-170000 + 82200) + (115600 – 103680)/1.1

+ (123760 – 94608)/1.1^2 +(115052 – 88608) / 1.1^3+ (109832 – 86304)/1.1^4

+ (109832 + 9800 – 84000) / 1.1^5= 5191ACCEPT.

2. Galaxy Satellite Co. is attempting to select the best group of independent projects competing for the firm's fixed capital budget of $10,000,000. All four projects have conventional cash flows. The firm’s cost of capital is 20%. A summary of key data about the proposed projects follows.

PV of Inflows

Project Initial Investment IRR at 20%

A $3,000,000 21% $3,150,000

B 9,000,000 25 9,320,000

C 1,000,000 24 1,040,000

D 7,000,000 23 7,350,000

E 4,000,00019% 3,875,000

F 6,000,00021% 6,500,000

What should the firm do?

Solution: For this question we can use either the profitability index or NPV of a combination of projects such that the total investment is 10 million (budget) or less. Since PI is the present value of benefits divided by the present value of costs, we can simply divide PV of inflows by the initial investment to obtain PI for each project:

PI for A: 3150000 / 3000000 = 1.05

B: 9320000 / 9000000 = 1.036

C:1040000 / 1000000 = 1.04

D: 7350000 / 7000000 = 1.05

E:3875000 / 4000000 = 0.969

F:6500000 / 6000000 = 1.08

All but project E is acceptable. Ranks: F, A and D (tied), C, B. We will have used up our 10 million dollar budget exactly by investing in projects F, A and C. Although D is ranked ahead of C we do not have the capital to invest in D.

3. Cuda Marine Engines, Inc. must decide whether a capital investment (new equipment) proposal is worthwhile. The firm has spent $15,000 developing the technology that will be applied to the new equipment. The proposed asset costs $50,000 and has installation costs of $3,000. The equipment will be housed in a facility that is owned by the firm but that is currently not being used. This facility is currently worth $10,000. The new equipment will be depreciated using a fiveyear recovery schedule, is expected to be used for 3 years after which it will be sold for $20,000. The new equipment is expected to generate revenues of $25,000 and operating expenses of $10,000 annually. It also requires an investment in inventory of $10,000. No other current accounts are expected to be affected. The firm has a 40 percent tax rate. If the required rate of return for this proposal is 15%, should Cuda go through with it?

Solution: Done in class.

4. A corporation is considering a capital project for the coming year.The project has an internal rate of return of 14 percent. If the firm has the following target capital structure and costs, what should their decision be and why?

Source of Capital Proportion Aftertax cost

______

Longterm debt .40 10 %

Preferred stock .10 15 %

Common stock equity .50 20%

Solution: We need to compare the IRR of the project to the WACC. The WACC is:

0.4 * 10% + 0.1 * 15% + 0.5 * 20% = 15.5%.

Since IRR < WACC, we would reject the project.

5. Kottinger's Kamp Supplies is considering an investment in new manufacturing equipment. The equipment costs $220,000 and will provide annual aftertax inflows of $80,000 at the end of each of the next four years. No terminal cash flows are expected. The firm's proportion of its capital structure that is debt is 25%. The remainder is common equity. The firm’s beta is 1.4, and its pretax cost of debt is based on the firm’s outstanding debt: Current price = $1040, Maturity = 15 years, Annual coupon rate = 7% (paid semi-annually). The current risk-free rate is 4% and the market return is 8%.

1. Assume the project is of approximately the same risk as the firm's existing operations. Should the firm invest?
2. Assume instead that KK is a multi-division firm with operations in Manufacturing, Travel Services, Retail Stores Rentals. Use the following information to determine whether the project should be accepted.

FirmIndustryBeta

StantonRetail 1.3

XenoxTravel Services0.7

Trail MixManufacturing2.2

Each of the firms above only operates in the industry indicated.

Solution: I did not provide you with a tax rate for this question. One is needed. Assume it is 35%.

1. For the first question, we can use the firm WACC to assess the project

Re = 4% + 1.4 * (8% - 4% ) = 9.6%

We can come up with an approximate value for the before-tax cost of debt using the firms outstanding debt information:

Rd =

WACC = 0.75 * 9.6% + 0.25 * 6.6% * (1 – 0.35) = 8.27%

The NPV of the project is:

NPV = -220 – 80/1.0827- 80/1.0827^2- 80/1.0827^3- 80/1.0827^4 = 43,485

Project is acceptable.

1. For the second question, we need to determine a project-specific WACC. Since the project is in manufacturing, we can use Trail Mix’s beta to compute a cost of equity and WACC for the project. Trail Mix represents a pure play firm for evaluating the project.

Re for project: 4% + 2.2 * (8% - 4%) = 12.8%

WACC = 0.75 * 12.8% + 0.25 * 6.6% * (1-0.35) = 10.67%

NPV = -220 – 80/1.1067- 80/1.1067^2- 80/1.1067^3- 80/1.1067^4 = 29955

Project is still acceptable.

6. Which of the following firms will benefit from an increase in debt in their capital structure? The firms’ tax rate is 35%

FirmBetaCost of equityReturn on Equity Before Tax cost of debt

A1.3 11.520%7%

B1.1 10.515%13%

C2.1 15.513%10%

D0.8 9.07%8%

E0.5 7.56%10%

Solution: Firms will benefit by adding debt if their return on equity is greater than their after-tax cost of debt.

Firm ROEAT cost of debt

A20%7% * (1-0.35) = 4.55%BENEFIT

B15%13% * (1-0.35) = 8.45%BENEFIT

C13%10% * (1-0.35) = 6.5%BENEFIT

D7%8% * (1-0.35) = 5.2%BENEFIT

E6%10% * (1-0.35) = 6.5%WILL NOT BENEFIT