Unit quiz: Terms That Change the Price: Refinancing, Resets, Leases, Currency and Guarantees

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Question 1

A borrower has $196,000 outstanding on a loan at 6.25 percent with 180 monthly payments left, so the payment is $1,680.55. A lender offers 5.50 percent over a fresh 180 months, charging closing costs of $4,200 and a prepayment penalty of 1.5 percent of the balance. Compute the new payment, the monthly saving and the number of months before the upfront cost is recovered.The penalty is $2,940 and the new balance is $203,140, so the payment is $1,659.82, the saving is $20.73 a month, and the break-even is 344.5 months, which is longer than the 180-month term, so the refinance never recovers its costThe rate falls by 0.75 percentage points on $196,000, which is about $1,470 a year, so the $7,140 of upfront cost is recovered in under five years and the refinance is clearly worthwhile

Question 2

A 5/1 adjustable-rate mortgage of $280,000 started at 5.75 percent over 360 months, giving a payment of $1,634.00. At the first reset the index is 5.20 percent, the margin is 2.50 percent, the initial cap is 2.00 percentage points and the balance is $259,734.12 with 300 months left. Compute the rate that applies and the new payment.The rate resets to the 7.75 percent initial cap because the cap is the rate the lender is entitled to charge, so the payment becomes about $2,020 and the increase is 23.6 percentThe fully indexed rate is 7.70 percent, which sits below the 7.75 percent initial cap, so 7.70 percent applies and the payment becomes $1,953.33, an increase of $319.33 or 19.54 percent

Question 3

A business can lease a machine for 48 monthly payments of $1,540 with no residual, or borrow $64,000 at 8.00 percent over 48 months and buy it. Total lease payments are $73,920 and total loan payments are $74,996.50. Compute the interest rate implicit in the lease and state which option is cheaper.The 48 payments of $1,540 discount to $64,000 at 7.25 percent a year, so the lease carries an implicit rate 0.75 points below the 8.00 percent loan and costs $1,076.50 less in total paymentsThe lease is cheaper because $73,920 is less than $74,996.50, and the implicit rate is 8.00 percent because that is the rate the bank quoted on the equivalent loan

Question 4

A US exporter expects EUR 900,000 in 120 days. The spot rate is 1.0790 dollars per euro and the 120-day forward is 1.0725. Compute the dollars locked in by the forward, the cost of cover against the spot rate, and the annualised cost. Then state the outcome if the spot rate is 1.0400 at payment.The forward costs 0.65 cents per euro, which is 0.65 percent, and since that is the annual cost of cover the exporter pays about 0.65 percent a year for certaintyThe forward locks $965,250 against $971,100 at spot, a cost of $5,850 or 0.60 percent over 120 days, which annualises to about 1.83 percent, and if spot falls to 1.0400 the unhedged receipt is $936,000, which is $29,250 below the forward

Question 5

A owner personally guarantees 100 percent of a $400,000 business loan. The lender's own data imply a 3 percent annual probability of default and 25 percent recovery in the event of default. Compute the expected loss on the guarantee and the annual debt service the owner would face if the guarantee were called at 8 percent interest-only.Expected loss is $400,000 multiplied by 0.03 multiplied by 0.75, which is $9,000 a year, while a call would put $32,000 of annual interest on the owner, or 26.7 percent of $120,000 of personal incomeExpected loss is $12,000, because 3 percent of $400,000 is $12,000 and the guarantee covers the whole balance

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