17. Your mortgage has 25 years left, and has an APR of 7.625% with monthly payme

Question

17. Your mortgage has 25 years left, and has an APR of 7.625% with monthly payments of $1449.

a. What is the outstanding balance?

b. Suppose you cannot make the mortgage payment and you are in danger of losing your

house to foreclosure. The bank has offered to renegotiate your loan. The bank expects to get

$150,000 for the house if it forecloses. They will lower your payment as long as they will

receive at least this amount (in present value terms). If current 25-year mortgage interest

rates have dropped to 5% (APR), what is the lowest monthly payment you could make for

the remaining life of your loan that would be attractive to the bank?

22. You need a new car and the dealer has offered you a price of $20,000, with the following payment

options: (a) pay cash and receive a $2000 rebate, or (b) pay a $5000 down payment and

finance the rest with a 0% APR loan over 30 months. But having just quit your job and started

an MBA program, you are in debt and you expect to be in debt for at least the next 21%u20442 years.

You plan to use credit cards to pay your expenses; luckily you have one with a low (fixed) rate of

15% APR (monthly). Which payment option is best for you?

28. Consider a project that requires an initial investment of $100,000 and will produce a single

cash flow of $150,000 in five years.

a. What is the NPV of this project if the five-year interest rate is 5% (EAR)?

b. What is the NPV of this project if the five-year interest rate is 10% (EAR)?

c. What is the highest five-year interest rate such that this project is still profitable?

37. Your best friend consults you for investment advice. You learn that his tax rate is 35%, and he

has the following current investments and debts:

%u25A0 A car loan with an outstanding balance of $5000 and a 4.8% APR (monthly compounding)

%u25A0 Credit cards with an outstanding balance of $10,000 and a 14.9% APR (monthly

compounding)

%u25A0 A regular savings account with a $30,000 balance, paying a 5.50% EAR

%u25A0 A money market savings account with a $100,000 balance, paying a 5.25% APR (daily

compounding)

%u25A0 A tax-deductible home equity loan with an outstanding balance of $25,000 and a 5.0%

APR (monthly compounding)

a. Which savings account pays a higher after-tax interest rate?

b. Should your friend use his savings to pay off any of his outstanding debts? Explain.

Explanation / Answer

Hi,

Please find the answer as follows:

Part 1:

a):

Monthly Discount Rate = .07625/12 = .00635

Present Value = R(1-(1+i)^-n)/i

Substituting Values in the above mentioned formula, we get:

Present Value =1449*(1-(1+0.00635)^-300)/0.00635 = 194024.14 or 194024

b)

Monthly Discount Rate = .05/12 = .00417

Present Value = R(1-(1+i)^-n)/i

Substituting Values in the above mentioned formula, we get:

Present Value ==150000/((1-(1+0.00417)^-300)/0.00417) = 877.23 or 877

Part 2:

Monthly Interest Rate = 15/12 = 1.25%

Present Value = -5000 + R(1-(1+i)^-n)/i = -5000 - 15000/30*(1-(1+.0125)^-30)/.0125 = -5000 - 12444.45 = -17444.45 or -17444

It is better to take the loan from the dealer.

Part 3:

a) NPV = -100000+150000/(1.05)^5 = 17528.93 or 17529

b) NPV = -100000+150000/(1.10)^5 = -6861.60 or -6862

c) You need to calculate IRR in this case which would be: 8.447 or 8.45%

Part 4:

a)

Regular Savings Account Interest Rate after Taxes = 5.50*(1-.35) = 3.575 or 3.58%

Money Market Savings Account = (1+.0525/365)^365 -1 = 5.389 or 5.39*(1-.35) = 3.50%

Regular savings account provides the higher rate of interest.

b) The amount of savings should be used to pay off both the credit card and car loans, as their costs are higher than the after tax savings interest rate as calculated above.

Thanks.

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