Question

You are a credit manager for Second Bank of Terlingua. Your bank is considering a loan to Arti Choke, a property developer in Terlingua. The structure of the loan is such that Arti would agree to pay back $13 million per year for 7 years, with the first payment in one year. Given the risk of Arti’s company, you think that the appropriate interest rate should be 23% per year, compounded annually. Given this rate and the structure of the loan, how much should your bank lend to Arti? Do not round at intermediate steps in your calculation. Report your answer in millions of dollars, rounded to three decimal places. Enter your answer without the $ symbol.

Answer 1

Max Loan = PV of annuity.

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$ 13,000,000.00
Int Rate	23.0000%
Periods	7

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 13000000 * [ 1 - [(1+0.23)^-7]] /0.23
= $ 13000000 * [ 1 - [(1.23)^-7]] /0.23
= $ 13000000 * [ 1 - [0.2348]] /0.23
= $ 13000000 * [0.7652]] /0.23
= $ 43251469.83
Loan can be availed is $ 43,251,469.83