# Loan + IRCap

In 90 days, a firm wishes to borrow \$10 million for 180 days. The borrowing rate is LIBOR plus 200 basis points. The current LIBOR is 4%. The firm buys an interest-rate call that matures in 90 days with a notional principal of \$10 million, 180 days in underlying, and a strike rate of 4.1%. The call premium is \$9,000. What is the effective annual rate of the loan if at expiration LIBOR = 4%? A) 0.0637. B) 0.0619. C) 0.0787. Please show your calculations…

Sheeztz noone? In 60 days, a bank plans to lend \$10 million for 180 days. The lending rate is LIBOR plus 200 basis points. The current LIBOR is 4.5%. The bank buys an interest-rate put that matures in 60 days with a notional principal of \$10 million, days in underlying of 180 days, and a strike rate of 4.3%. The put premium is \$4,000. What is the effective annual rate of the loan if at expiration LIBOR = 4.1%? A) 0.0640. B) 0.0648. C) 0.0619.

B) 6.19% Interest on loan (paid at end of 180 days)= 0.5 * 6% of \$10 million = \$300000 Call option expires worthless since current LIBOR (4%) greater than strike LIBOR of 4.1% Call option premium cost = \$9000 FV of \$9000 at end of loan period (90 days till call expiration + 180 days loan period) = 9000 (1 + .06 * (270/360)) = \$9405 Total effective loan cost = \$300000 + 9045 = 309405 Effective interest rate = 309405 / 10000000 = 3.09405 % Annualised = 2 * 3.09405% = 6.188% Havent used any textbook formulae so not sure

Where in the CFAI text is the section which covers these questions?

B? 1st step is to calculate the FV of the premium: 9,000*[1+(.04+.02)*90/365] = 9,133 2nd step if to calculate the pay-off, if any. In this case, there is none, so we calculate just the interest during the period: (.02+.04)*(180/365)*10,000,000 = 295,890 3rd step: calculate the interest = (9,133 + 295,890 + 10,000,000)/10,000,000 = 1.0305 Square this for effective interest = 6.19%

B and C?

A for the second problem?

sparty show me the calculation for second problem

I am going A and A I think you use 360 days for the option permium and amount owed on the loan, then use 365 when you annualize the number. So for the first problem it is Interest on loan (paid at end of 180 days)= 0.5 * 6% of \$10 million = \$300000 Call option expires worthless since current LIBOR (4%) greater than strike LIBOR of 4.1% Call option premium cost = \$9000 FV of \$9000 at end of period (90 days till loan starts) = 9000 (1 + .06 * (90/360)) = \$9135 Total amount borrowed = 10,000,000 - 9135 = 9990865 Total effective loan cost = 300000 +10,000,000 = 10,309,135 Effective interest rate = 10,309,135 / 9,990,865 = 3.0942 % Annualized = 1.030942^(365/180) = 6.3741%

Total amount borrowed = 10,000,000 - 9135 = 9990865 I guess you need to add the PV of premium in the loan, don’t you?

for the second, you need to subtract the premium from the option. 1st step, calculate the fv of premium = 4,043 2nd step: calculate the interest = 300,822 3rd step: calculate option pay-off = 9,863 4th: calculate interest = (300,822+9,863+10,000,000)/(10,000,000-4,043) square the result = 6.4%

When you are receiving a loan you subtract the FV of the Call option, but when you are giving a loan you add the FV of the Put option… the only thing that is compounded at 365 days is the annualization in the last step of the problem.

Hi Boston, Does that mean my answers are wrong? I didn’t subtract the FV from the denominator for the first problem, and subtracted it for the second one.

Boston is correct. You need to subtract the FV of the premium from the borrowed amount to get the effective borrowing amount. From here, you run through the calculations and come up with: (10,300,000/9,990,868)^(365/180) - 1 = 6.374% Correct answer being A.

please see this post, http://www.analystforum.com/phorums/read.php?13,912100,913468#msg-913468 It has the same example, but explanation by CFALEB is very nicely done

So for the first problem, you subtract the FV from the total amount and for the second problem, you add the FV to the total amount. Right?

Correct Sparty… in the first example you are receiving a loan, which is an inflow, but you have to pay the cost of the option, which is an outflow… So you receive 10 million but have to pay about 9000… in the second example you are extending a loan which is an outflow, and you have to pay the option premium which is another outflow…so you give 10 million and also have to pay about 4000…

sparty419 Wrote: ------------------------------------------------------- > for the second, you need to subtract the premium > from the option. > > 1st step, calculate the fv of premium = 4,043 I got that. > > 2nd step: calculate the interest = 300,822 I calculated the interest = 10,000,000* [( .041+.02)(180/360)] = 305,000 > > 3rd step: calculate option pay-off = 9,863 option payoff = 10,000,000[( .002)(180/360)] = 10,000 > > 4th: calculate interest = > (300,822+9,863+10,000,000)/(10,000,000-4,043) > > square the result = 6.4% Am I correct?

I know Team-AF does not need any answer or guidelines, but here’s a copy paste just for the heck of it. Your answer: B was incorrect. The correct answer was A) 0.0637. The call option is out-of-the-money. The implied net amount to be borrowed after the cost of the call is: \$9,990,865 =\$10,000,000 - \$9,000 × (1 + (0.04+0.02) × (90/360)) For LIBOR = 0.04 at expiration, the dollar cost is: \$300,000 = \$10,000,000 × 0.06 × (180/360) The effective annual rate is: 0.0637 = (\$10,300,000 / \$9,990,865)(365/180) - 1 The effective amount the bank parts with or “lends” at time of the loan is: \$10,004,043 = \$10,000,000 + \$4,000 × (1 + (0.045 + 0.02) × (60/360)) If LIBOR at maturity equals 4.1%, the payoff of the put would be: payoff = (\$10,000,000) × [max(0, 0.043 – 0.041) × (180/360) payoff = \$10,000 The dollar interest earned is: \$305,000=\$10,000,000 × (0.041 + 0.02) × (180/360), and EAR = (\$10,000,000 + \$10,000 +\$305,000) / (\$10,004,043) - 1 EAR = 0.0640 or 6.40% Sorry for the delay, just reached home and have access to Qbank now. I am 0/2 here!

Thanks. Just as I thought.