IV. (16 points) A. Assume you have just taken out a new home mortgage. You will

Question

IV. (16 points) A. Assume you have just taken out a new home mortgage. You will borrow $200, 000 and make equal annual payments for 20 years. If the interest rate is 10% per year, how much will the payments be if you pay interest on the unpaid balance each year? (4 points) B. Construct an amortization schedule for the first two years. (8 points) End of Payment alance year 0 C. If you are in the 30 % marginal tax bracket, what will the net cash flow after tax to service this loan in the first year? (Think of yourself and your home mortgage and your income tax return) (2 points) s the net cash flow after tax needed to service this loan get larger or smaller in future time periods? D. Doe (2 points)

Explanation / Answer

A. The annual payments will be $ 23,492

Present value of an annuity = Annuity x PVIFA i, n

PVIFAi,n = [ { 1 - ( 1 / 1 + r) n} / r ]

PVIFA 10%, n=20 = [ { 1 - ( 1 / 1.10) 20} / 0.10 ] = 8.51356

Annuity = Present value of the annuity / PVIFA = $ 200,000 / 8.51356 = $ 23,492

B. Amortization Schedule for the first two years :

C. There would be no income tax implication for the principal component.

But there would be a tax benefit on the interest component.

In the first year, the net cash flows on the interest component = $ 20,000 x ( 1 - 0.30) = $ 14,000.

Net cash outflow in the first year = $ (14,000 + 3,492) = $ 17,492.

D. As the interest component gets smaller year on year, the net cash flow to service the loan gets larger over the future time periods.

Year Amount Paid Interest Reduction of Mortgage Payable Mortgage Payable $ $ $ $ 0 - - - 200,000 1 23,492 20,000 3,492 196,508 2 23,492 19,651 3,841 176,857

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