calculate annual mortgage payment

Question 1

You just took out a variable-rate mortgage on your new home. The mortgage value is \$100,000, the term is 30 years, and initially the interest rate is 8%. The interest rate is fixed for five years, after which time the rate will be adjusted according to prevailing rates. The new rate can be applied to your loan either by changing the payment amount or by changing the length of the mortgage.

a Assuming annual payments, what is the original annual mortgage payment?

b Prepare an amortization schedule for the first five years. What will be the mortgage balance after five years?

c If the interest rate on the mortgage changes to 9% after five years, what will be the new annual payment that keeps the termination time the same?

d Under the interest change in part (c), what will be the new term if the payments remain the same?

Question 2

John is considering the best capital structure for his firm. Suppose there are two capital structures for him to choose from. Structure A would have 7,000 shares of stock and \$160,000 in debt. Structure B would have 5,000 shares of stock and \$240,000 in debt. The interest rate on the debt is 10%.

a Ignoring taxes, compare both of these structures to an all-equity structure, assuming that EBIT will be \$39,000. The all-equity structure would have 11,000 shares of stock outstanding. Which of the three structures has the highest EPS? The lowest?

b In part (a), what are the break-even levels of EBIT for each structure as compared to that for an all-equity structure? Is one higher than the other? Why?

c Ignoring taxes, when will EPS be identical for Structures A and B?

d Repeat parts (a), (b) and (c) assuming that the corporate tax rate is

40%. Are the break-even levels of EBIT different from before? Why

or why not?

Question 3 (51 marks)

Read the text below and answer the questions that follow it. Protect-the-earth Company needs to raise \$3 million funds externally to finance the acquisition of a new water saving system. After carefully analysing alternative financing sources, Richard Kim, the firm's vice president of finance, reduced the financing possibilities to three alternatives: (1) debt, (2) debt with warrants, and (3) a financial lease. The key terms of each of these financing alternatives follow.

1 Debt

The firm can borrow the full \$3 million from First Shreveport Bank. The bank will charge 12% annual interest and require annual end-ofyear payments of \$1,249,050 over the next three years. It is determined that the amounts of the depreciation of the water saving system are \$1,000,000 (first year), \$1,350,000 (second year) and \$450,000 (third year). The firm will pay \$45,000 at the end of each year for a service contract that covers all maintenance costs; insurance and other costs will be borne by the firm. The firm plans to keep the equipment and use it beyond three years.

2 Debt with warrants

The firm can borrow the full \$3 million from Southern National Bank. The bank will charge 10% annual interest and will, in addition, require a grant of 50,000 warrants, each allowing the purchase of two shares of the firm's stock for \$30 per share at any time during the next ten years. The stock is currently selling for \$28 per share, and the warrants are estimated to have a market value of \$1 each. The price (market value) of the debt with the warrants attached is estimated to equal the \$3 million initial loan principal. The annual end-of-year payments on this loan will be \$1,206,345 over the next three years. Depreciation, maintenance, insurance, and other costs will have the same costs and treatments under this alternative as those described before for the straight debt financing alternative.

3 Financial lease

The water saving system can also be leased from First International Capital. The lease will require annual end-of-year payments of \$1,200,000 over the next three years. All maintenance costs will be paid by the lessor; insurance and other costs will be borne by the lessee. The lessee will exercise its option to purchase the system for \$220,000 at termination of the lease at the end of three years. Richard decided first to determine which of the debt financing alternatives - debt or debt with warrants - would least burden the firm's cash flows over the next three years. In this regard, he felt that very few, if any, warrants would be exercised during this period. Once the better debt financing alternative was found, Richard planned to use

lease-versus-purchase analysis to evaluate it in light of the lease

Assignment File 3

alternative. The firm is in the 40% tax bracket, and its after-tax cost of

debt would be 7% under the debt alternative and 6% under the debt

with warrants alternative.

Source: adapted from Gitman, L J (2006) Principles of Managerial Finance,

11th edn, Pearson, 742-43.

Required:

a Under the debt with warrants, find the following:

i straight debt value

ii implied price of all warrants

iii implied price of each warrant

iv theoretical value of a warrant.

b On the basis of your findings in part a, do you think the price of the

debt with warrants is too high or too low? Explain.

c Assuming that the firm can raise the needed funds under the specified

terms, which debt financing alternative - debt or debt with warrants

- would you recommend in view of your findings above? Explain.

d For the purchase alternative, financed as recommended in part (c),

calculate the following:

i the annual interest expense deductible for tax purposes for each

of the next three years

ii the after-tax cash outflow for each of the next three years

iii the present value of the cash outflows using the appropriate

discount rate.

e For the lease alternative, calculate the following:

i the after-tax cash outflow for each of the next three years

ii the present value of the cash outflows using the appropriate

discount rate applied in part (d)(iii).

f Compare the present values of the cash outflow streams for the

purchase - in part (d)(iii) - and lease - in part (e)(ii) -

alternatives, and determine which would be preferable. Explain and

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