variable-rate mortgage

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Question 1 You just took out a variable-rate mortgage on your new home. Themortgage value is $100,000, the term is 30 years, and initially the interestrate is 8%. The interest rate is fixed for five years, after which time therate will be adjusted according to prevailing rates. The new rate can beapplied to your loan either by changing the payment amount or bychanging the length of the mortgage.a Assuming annual payments, what is the original annual mortgagepayment? b Prepare an amortization schedule for the first five years. What will bethe 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 timethe same? d Under the interest change in part (c), what will be the new term if thepayments remain the same? Question 2 John is considering the best capital structure for his firm. Suppose thereare two capital structures for him to choose from. Structure A wouldhave 7,000 shares of stock and $160,000 in debt. Structure B would have5,000 shares of stock and $240,000 in debt. The interest rate on the debtis 10%.a Ignoring taxes, compare both of these structures to an all-equitystructure, assuming that EBIT will be $39,000. The all-equitystructure would have 11,000 shares of stock outstanding. Which ofthe three structures has the highest EPS? The lowest? b In part (a), what are the break-even levels of EBIT for each structureas compared to that for an all-equity structure? Is one higher than theother? 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 is40%. Are the break-even levels of EBIT different from before? Whyor 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 externallyto finance the acquisition of a new water saving system. Aftercarefully analysing alternative financing sources, Richard Kim, thefirm’s vice president of finance, reduced the financing possibilities tothree alternatives: (1) debt, (2) debt with warrants, and (3) a financiallease. The key terms of each of these financing alternatives follow.1 DebtThe firm can borrow the full $3 million from First Shreveport Bank.The bank will charge 12% annual interest and require annual end-ofyearpayments of $1,249,050 over the next three years. It is determinedthat the amounts of the depreciation of the water saving system are$1,000,000 (first year), $1,350,000 (second year) and $450,000 (thirdyear). The firm will pay $45,000 at the end of each year for a servicecontract that covers all maintenance costs; insurance and other costswill be borne by the firm. The firm plans to keep the equipment anduse it beyond three years.2 Debt with warrantsThe firm can borrow the full $3 million from Southern National Bank.The bank will charge 10% annual interest and will, in addition, requirea grant of 50,000 warrants, each allowing the purchase of two sharesof the firm’s stock for $30 per share at any time during the next tenyears. The stock is currently selling for $28 per share, and the warrantsare estimated to have a market value of $1 each. The price (marketvalue) of the debt with the warrants attached is estimated to equal the$3 million initial loan principal. The annual end-of-year payments onthis loan will be $1,206,345 over the next three years. Depreciation,maintenance, insurance, and other costs will have the same costs andtreatments under this alternative as those described before for thestraight debt financing alternative.3 Financial leaseThe water saving system can also be leased from First InternationalCapital. The lease will require annual end-of-year payments of$1,200,000 over the next three years. All maintenance costs will bepaid by the lessor; insurance and other costs will be borne by thelessee. 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 financingalternatives — debt or debt with warrants — would least burden thefirm’s cash flows over the next three years. In this regard, he felt thatvery few, if any, warrants would be exercised during this period. Oncethe better debt financing alternative was found, Richard planned to uselease-versus-purchase analysis to evaluate it in light of the leaseAssignment File 3alternative. The firm is in the 40% tax bracket, and its after-tax cost ofdebt would be 7% under the debt alternative and 6% under the debtwith 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 thedebt with warrants is too high or too low? Explain. c Assuming that the firm can raise the needed funds under the specifiedterms, 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 eachof the next three years ii the after-tax cash outflow for each of the next three yearsiii the present value of the cash outflows using the appropriatediscount rate. e For the lease alternative, calculate the following:i the after-tax cash outflow for each of the next three yearsii the present value of the cash outflows using the appropriatediscount rate applied in part (d)(iii). f Compare the present values of the cash outflow streams for thepurchase — in part (d)(iii) — and lease — in part (e)(ii) —alternatives, and determine which would be preferable. Explain anddiscuss your recommendation.

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