Question

1. If you lease a $57,000 car with a $700 per month payment and its projected residual value is $37,000 at the end of the three year leasing period, what is the implied interest rate?

Logic = you receive something worth $57,000 in period zero (PV positive inflow); you make monthly payments of $700 (negative PMT because it is an outflow) and you give that car back at the end of three years (n = 3 x12 months) which is worth $37,000 (negative FV because again it is an outflow).

2. If you pay $4 for a call option on JPM stock with an at the money strike price of $100 and at the same time you write a call option with a strike price of $110 for which you receive $1; how much money do you make or lose on the transaction if the stock goes to either $120; $105; or $90?

Answer 1

1.
Using financial calculator
PV=57000
PMT=-700
FV=-37000
N=3*12=36
CPT I/Y=0.304%

Hence, implied annual interest rate=0.304%*12=3.652%

2.
Profit=MAX(Stock price at expiry-100,0)-MAX(Stock price at expiry-110,0)-4+1

120:
=MAX(120-100,0)-MAX(120-110,0)-4+1
=7

105:
=MAX(105-100,0)-MAX(105-110,0)-4+1
=2

90:
=MAX(90-100,0)-MAX(90-110,0)-4+1
=-3