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# Cost of Capital Problem

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Current Balance Sheet
Assets \$100 Debt \$10
Equity \$90

Debt/Assets After-Tax Cost of Debt Cost of Equity Cost of Capital
0% 8% 12% ?
10% 8% 12% ?
20% 8% 12% ?
30% 8% 13% ?
40% 9% 14% ?
50% 10% 15% ?
60% 12% 16% ?

What is the firm's weighted-average cost of capital at various combinations of debt and
equity, given the above information?
cost of capita (k) = (weight) (cost of dept) + (weight) (cost of equity)
k = (0) .08 + (0) .12 = 0 IS THIS CORRECT

Construct a pro forma balance sheet that indicated the firms optimal capital structure.
Compare this balance sheet with the firm's current balance sheet. What course of action
should the firm take?

Assets \$100 Debt \$ ?
Equity \$ ?

As a firm initially substitues debt for equity what happens to the cost of capital, and why?

If a firm uses too much debt financing, why does the cost of capital rise?

https://brainmass.com/economics/personal-finance-savings/cost-of-capital-problem-87917

#### Solution Preview

Current Balance Sheet
Assets \$100 Debt \$10
Equity \$90

Debt/Assets After-Tax Cost of Debt Cost of Equity Cost of Capital
0% 8% 12% 12%
10% 8% 12% 11.60%
20% 8% 12% 11.20%
30% 8% 13% 11.50%
40% 9% 14% 12%
50% 10% 15% 12.50%
60% 12% 16% 13.60%

What is the firm's weighted-average cost of capital at various combinations of debt and
equity, given the above information?

cost of capita (k) = (weight) (cost of debt) + (weight) (cost of equity)

First, we need to know that ASSET = DEBT + EQUITY. Therefore, when Debt/Assets ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer the request of the assignment in excel file.

\$2.19

## Capital Budgeting & Investment problems

Question 1
Apex Ltd. is an Australian operated company with mainly American resident shareholders. The company is currently in the process of comparing two mutually exclusive machines for use in a new project with Machine A costing \$30,000, having a useful life of five years and machine B costing \$45,000 and having a useful life of 10 years.
Cash inflows from sales are expected to be \$22,000 p.a. from each machine, while total cash-based operating costs are expected to be \$10,000 and \$8,000 respectively for each machine. All revenues and costs are assumed to occur at the end of the respective years for simplicity of assessment. Machine A is expected to have a salvage value of \$4,000 at the end of 5 years, while at the end of 10 years machine B will be worthless. Depreciation for accounting and tax purposes is calculated on a straight-line basis on the original cost of each machine with no consideration in depreciation calculations for any expected salvage value.
The company has an after-tax required rate of return of 14% and pays income tax at the rate of 40% in the year following the year of income (that is, taxes levied on year 1 income are paid at the end of year 2)

Required -
a) Provide some reasons as to why the alternative machines are said to be mutually exclusive for the company.

b) Record the relevant cash-flows for each machine on a time (cash-flow) diagram.

c) Advise the company which machine (if any), should be purchased and justify all the processes you have used in order to reach your decision.

d) i) If Apex Ltd., prior to finalising the decision as to which machine (if any), should be purchased, was taken over by a group of Australian resident shareholders, resulting in the company becoming fully Australian owned, briefly discuss what difference this would make (if any) to your calculations in part c) of this question.
ii) Perform any relevant calculations relating to this part of the question and advise the company whether your decision from part c) of this question will now change.

Question 2
You are considering two mutually exclusive projects. The expected values for each project's end-of-year cash flows are:

Year Project A Project B
0 -\$1,000,000 -\$1,000,000
1 500,000 500,000
2 700,000 600,000
3 600,000 700,000
4 500,000 800,000
You have decided to evaluate these projects using the certainty equivalent method. The certainty equivalent coefficients for each project's cash flows are given below:
Year Project A Project B
0 1.00 1.00
1 0.95 0.90
2 0.90 0.70
3 0.80 0.60
4 0.70 0.50

Required :
a) Given that the risk-free rate of return is 5%p.a., what is the NPV of each project?

b) Briefly discuss and justify which project, if any, should be preferred.

c) In practice, what factors are likely to influence the selection of the certainty equivalent coefficients for each project's expected cash flows?

Question 3
Mr. Huey Lewis met with his accountant recently and the accountant strongly advised Huey to invest in Australis Exploration Solutions, an Australian high technology listed public company specialising in filtering out dust particles in mine shafts and thus reducing worker exposure to bacteria etc.

The advice was based on the accountant obtaining a preview of the company's soon to be released financial statements which had reported a significant increase in its accounting revenues and profit margins in the most recent reporting period. The accountant, who was a recent MBA graduate (from an online program offered by a recently established Banga University), also advised your neighbour that, according to the company's most recent balance sheet, it held assets valued 10 times greater than its liabilities.

Included in the company's assets was the recently revalued amount (from \$100,000 to \$1 million) of some vacant land attached to the building that the company currently operates its business from. The company directors had established the revalued amount based on average sales in the local area over the last 5 years.

The accountant fortuitously had a client who was seeking to sell their current holding in Australis Communications.com and would accept a price of only \$3 per share from Mr. Lewis, given that the client had an outstanding tax bill that needed to be paid quickly. Although Mr. Lewis has no reason to doubt the word of his accountant, he has sought your advice prior to undertaking the investment as he is aware of your current study in a finance course at University.

Required :

Based on the information given, what would be your advice to your neighbour about undertaking the investment described above? You are welcome to make any assumptions reasonably necessary in order to provide an informed response.

Note: Your discussion would be expected to be based on your critical interpretation and analysis of the specific information provided above together with any reasonable assumptions that allow for the development of an informed response.

Question Number 4

The Dayana Company is planning on issuing a debenture that pays no interest but can be converted into a face value of \$1,000 at maturity, 8 years from their issue date. To price these debentures competitively with other bonds of equal risk, it is determined that they should yield 9%, compounded annually.

Required :
a) At what price should the Dayana Company currently sell these debentures?

b) If you purchased these debentures on the issue date from the Dayana Company in part a) of this question, what would be your sale price after holding the bonds for 3 years given the following information available at the time of sale (3 years after the date of issue) :
- Government bonds having a par value of \$1,000 with a 5 year term are able to be issued at a yield of 5% with annual coupon payments in arrears of \$60.
- Dayana Company at this time was in the process of issuing a 5 year
debenture (using the same form of security as previously to debenture
holders), having a par value of \$500, with quarterly coupon payments to
debenture holders in advance of \$14 per payment. The issue price for
these debentures was to be \$485.
Show all calculations (including a cash-flow diagram) and justify any assumptions included in the relevant calculations made.

c) Which, if any, of the information included in part b) of this question was not used in calculating the sale price required by part b) ? Justify your response.

Question Number 5

If the nominal rate of interest is 14.2% p.a. and the anticipated rate of inflation is 5.5% p.a., what is the real rate of interest to the nearest 0.1% ?

b) Explain to an inexperienced investor, your interpretation of a real rate of interest.

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