Question

Your mother and father are retired and need income to live on. The local financial advisor offers to sell them a product that will provide them $75,000 a year for 15 years. Prevailing interest rates are 8%. The cost to purchase the product is $750,000.
They asked you to evaluate the offer. Do you recommend they purchase the product? Why?
If prevailing interest rates were 5%, would it change your recommendation? Why?

Answer 1

Answer:

To evaluate the choice, we have to calculate the present value of future cash flows and compare it with the cost. We use the following formula

    present value    =  C ×  [ $\frac{1 - (1 + i)^{-n} }{i}$ ]​

where

                     C = yearly payments = 75000

                     i =  interest rate  = 8%

                     n = no. of years   = 15

put the given values in above equation, we get

       Present value = 75000 ×8.559478688

                               = 641,961

Since the present value of cash flow 641,961 is less than the cost 750,000, I would not recommend it.

If Interest rate = 5%, then:

Do the same procedure as above but take i=5%

        Present value = 75000 × 10.37965804

                                = 778,474

Since the present value of future cash flows 778,474 is greater than the cost 750,000, I would recommend it.