Question

Dr Jones is evaluating an offer for his medical practice that will allow him to retire five years early. He has received an offer of R650 000 for his practice and he can invest this amount in an account earning 15% per year, compounded annually. If the practice is expected to generate the following cash flows, advise Dr Jones as to whether he should accept this offer and retire now or not.  

End of year	Amount (in rands)
1	160 000
2	160 000
3	130 000
4	130 000
5	100 000

Answer 1

If the practice is expected to generate the following cash flows, advise Dr Jones as to whether he should accept this offer and retire now or not?

Answer: Accept the offer and retire now

                (Because this option gives him higher future value)

Working

In order to compare the given options we need to bring all options into same time line. This can be comparing the present value of both options or future value of both the options. We will compare the future value of both the options available to Dr. Jones.

Formula for calculating future value is as follows;

Future Value = Cash Flow * (1 + R)^N

Where,

R = Interest rate

N = Number of years

Future value of 650,000 received today at the end of 5^th year.(Retire 5 years early option)

Future Value      = 650,000 * (1.15)⁵

                                = 650,000 * 2.0114

                                = 1,307,410

(Note: Cash flow is the amount received = 650,000., R = 15% (provided in the question) and N = 5 years)

Future value of continue practice option.

We will compare total future value of all the future cash flows at the end of 5^th year. Since interest rate is not provided for this option separately we assume interest rate of 15% per annum is applicable for this option also.

Year	Cash flows	Workings	Future Value	Notes
1	160,000	FV = 160,000*(1.15)4	279,841	(cash flows is received at the end of 1st year so period will be 4 years)
2	160,000	FV = 160,000*(1.15)3	243,340	(cash flows is received at the end of 2nd year so period will be 3 years)
3	130,000	FV = 130,000*(1.15)2	171,925	(cash flows is received at the end of 3rd year so period will be 2 years)
4	130,000	FV = 130,000*(1.15)1	149,500	(cash flows is received at the end of 4th year so period will be 1 years)
5	100,000		100,000	(Since amount is received at the end of 5th year its self so future value is same as cash flow its self)
		Total Future Value	944,606

Total Future value of continue practice option is 944,606

Whether he should accept this offer and retire now or not?

Since future value of continue practice option is less than the retire 5 years early option, he should retire now.

Future value of 2 options

Options	Future value
Retire 5 years early – i.e. 650,000 received now	1,307,410
Future value of continue practice option	944,606