Question

You are the manager of a bank. You need to decide whether to approve a 10-year loan application from a 25 year old student to finance her MBA. The loan will yield a loss of $250 per year to the bank for the duration of the loan. After 10 years, the student will likely buy other products and therefore she will yield a profit of $500 per year until she is 65. After age 65, she will yield a profit of $1,000 per year until she is 85, when she will stop being a customer. The likelihood that she stops being a customer after she repays her MBA loan is 2% each year. The discount rate that the bank uses is 7% per year.

Would you approve the loan? Please explain with numerical support.

Answer 1

Answer and Explanation:

The computation is shown below:

Present value of loss because of giving the loan to her is

= PVAF (7%, 10 years) × $250

= 7.02358 × $250

= $1,755.9

Now

The Present value of gain after repayment of the loan is

Till age of 65

($500, age 35 years to 65 years i.e. 30 years) is

= [PVAF (7%, 40 years) - PVAF (7%, 10 years)] × 0.98 (probability of failure) × $500

= (13.3317 - 7.02358) × 0.98 × $500

= $3,090.98 (A)

Till age of 85

($1000, age 65 years to 85 years i.e. 20 years)

= [PVAF (7%, 60 years) - PVAF (7%, 40 years)] × 0.98 (probability of failure) × $1,000

= (14.03918 - 13.3317) × 0.98 × $1,000

= $693.33 (B)

Now

Expected inflow from the student post repayment of the loan is

= (A) + (B)

= $3,784.31

Now expected net gain is

= $3,784.31 - $1,755.9

= $2,028.41

Here we exclude the period from 25 to 35 years and at later from 25 years to 65 years