1) You want to borrow money to purchase a new home at a price of $300,000, and would like to borrow an 80% loan to finance it. You can obtain a fixed rate, fully amortizing loan for 30 years at 4.0% interest rate, to be paid in monthly payments. Moreover, you will pay 2 discount points for the loan.
- What is the monthly payment for the loan? (Answer: $1,145.8)
- What is the effective interest rate if you pay off the mortgage after 30 years?(Answer: I = 4.17%)
- If you plan to repay the loan after 5 years (no prepayment penalty), what is the effective interest rate? (Answer: I = 4.47%; Outstanding balance after 5 years: 217,073.81)
- Suppose you and the lender agree on monthly payments during the first year to be $700. What would be the outstanding loan balance at the end of first year? (Answer: FV = $241,222.2)
2) You want to borrow from a bank to finance a commercial real estate investment. You consider an ARM for $100,000 at the following terms: 1) initialinterest rate (year 1; not initial index) = 9%; 2) margin = 2%; 3) loan term = 15 years; 4) frequency of adjustment = 1 year (monthly compounding); 5) interest rate cap = none; 6) payment cap = none; and 7) discount points = 2%; 8) no negative amortization is allowed. The index rates (based on 1 year treasury rate) for each of next two years are expected to be 11% and 8%, respectively.
- If the loan is repaid after 3 years, what would be the monthly payments and the ending loan balances for each of the three years?
Year Beginning Bal. N PMT I Ending Bal.
1 $100,000 180 $1014.3 9 $96,695
2 $96,695168 $1252 13 $94,083
3 $94,083 156 $1079.9 10 $90,364
(b) What is the effective interest rate for this mortgage? (Answer: IRR = 11.44% if entered as monthly payments; IRR=11.30% if summed up for each year; Hint: When entering the cash flows as monthly, use a frequency of 12 for the first two years’ cash flows, 11 for the third year’s and 1 for the last payment plus the loan repayment. In the exam, you only have to calculate IRRs based on annual cash flows.)
(c) Suppose that there is an annual interest rate cap of 2% specified in the loan contract. What would be the effective interest rate for this mortgage? (Answer: payment year 2: $1,130; payment year 3: $1,074.5; IRR = 10.77% monthly; IRR= 10.63% annualized)
3) You conduct an investment analysis for a retail building you plan on holding for 6 years and have the following after-tax cash flows. Your required rate of return is 10%.
- What is the NPV? (Answer: $113,554.94)
- What is the IRR? (Answer: 11.71%)
- What is the NPV if the required return is 12%? (Answer: -$18,192.88)
4) Sally took a mortgage loan 5 years ago for $200,000 at 6.5% interest rate for 15 years, to be paid in monthly payments, no discount points or fees. Now, a lender is offering her a new mortgage loan at 3.5% for 10 years. Suppose that a prepayment penalty of 3% must be paid if Sally refinances the old loan. Moreover, the lender who is making the new loan requires an origination fee of $3,500. Assume the fees and penalty have to be paid by Sally. As of today, Sally plans to hold the property for 10 years.
- What is the payment for the old loan? (Answer: PMT=$1,742.21)
- What is the outstanding loan balance after 5 years? (Answer: FV=$153,434)
- What would be the total financing cost (in dollar value, not include the loan amount itself)if she decides to refinance the old loan? (Answer: $8,103)
- What is the effective interest rate for the new loan? Should she refinance? (Answer: new loan balance = $161,537; mortgage payout (considering retained fees)=$158,037; I=96%; yes, she should refinance)