Question

1. Variable Interest Rates Jodie is a medical student who has accumulated 24,000$ of credit card debt on numerous she is offered the following debt consolidation plan: the bank will lend her 24,000s to 1/1/2012, and a payment of 8,000*(1+0.01+Prime Rate on 1/1/2013)S on 1/1/2013. It is the yearly rate for loans to prime borrowers, that is, borrowers who will almost credit cards. She is looking to consolidate her debt. On 1 /1/2010, she visits her bank and pay offall her outstanding credit card balances on that day, in return for a fixed payment of 11,520$ on 1/1/2011, plus a payment of 8,000*(1+0.01+Prime Rate on 1/1/2012)5 on The Prime Rate is a market loan rate that is quoted on all the major financial newspapers. certainly be able to pay back. Assume that the prime rate is 4.25% on 1/1/2012 and 7.50% on 1/1/2013. Compute the yield to maturity for Jodie's loan. Assume that the prime rate on 7.50% on 1/1/2012 and 4.25% on 1/1/2013. Compute the yield to maturity on Jodie's loan. Provide intuition on how the sequencing of interest payments affects the yield to maturity

Answer 1

Loan principal	24,000
Payments
1/1/2011	11,520
1/1/2012	8000*(1+0.01+PR12)
1/1/2013	8000*(1+0.01+PR13)
Case 1
Prime rates
1/1/2012	4.25%
1/1/2013	7.50%
Repayments
1/1/2012	8,420
1/1/2013	8,680
Total payment	28,620

Period	1/1/2010	1/1/2011	1/1/2012	1/1/2013
Cash flows	24,000	(11,520)	(8,420)	(8,680)
Yield on loan/ IRR	9.88%

Case 2
Prime rates
1/1/2012	7.50%
1/1/2013	4.25%
Repayments
1/1/2012	8,680
1/1/2013	8,420
Total payment	28,620

Period	1/1/2010	1/1/2011	1/1/2012	1/1/2013
Cash flows	24,000	(11,520)	(8,680)	(8,420)
Yield on loan/ IRR	9.93%

In case 2, lower amount is paid later in the life of the loan as the prime rate is lower as of 1/1/13 than that on 1/1/12. However, the yield is still higher in this case. This is because of the time value of money. Time value of money decreases as the time to receive it increases. Hence, when higher amount is received earlier in the life, it has more value and higher yield.