Question

As an investment advisor, you have been approached by a client called Kiprono, who wants some help in investment-related matters. Kiprono is currently 45 years old and has Ksh. 600,000 in the bank. He plans to work for 15 more years and retire at the age of 60. Kiprono’s present salary is Ksh. 400,000 per year. He expects his salary to increase at the rate of 12 percent per year until his retirement. Kiprono has decided to invest his bank balance and future savings in a portfolio in which stocks and bonds would equally be weighted. For the sake of simplicity, assume that these proportions will be maintained by him throughout. He also believes that bonds would provide a return of 7 percent and stocks a return of 13 percent. You concur with his assessment. Once he retires at the age of 60 he would like to withdraw Ksh. 500,000 per year from his investment for the following 15 years as he expects to live up to the age of 75 years. He also wants to bequeath Ksh. 1 million to his children at the end of his life.

Required

i. How much money would he need 15 years from now? ii. How much should Kiprono save each year for the next 15 years to be able to meet his investment objectives as shown above? Assume that the savings will occur at the end of each year.

iii. Suppose Kiprono wants to donate Ksh. 200,000 per year in the last three years of his life to a charitable cause. Each donation would be made at the beginning of the year. How much money would he need when he reaches the age of 60 to meet his specific need?

iv. Kiprono recently attended a seminar on human capital where the speaker talked about a person's human capital as the present value of his lifetime earnings. Kiprono is curious to find out the present value of his lifetime salary. For the sake of simplicity assume that his present salary of Ksh. 400,000 will be paid exactly one year from now, and his salary will be paid in installments. what is the present value of his lifetime salary, if the discount rate is 8 percent? Remember that he expects his salary to increase at the rate of 12 percent per year until his retirement. (Ignore the taxation)

Answer 1

His return from the equally weighted portfolio=

(50%*7%)+(50%*13%)=

10.00%

i. How much money would he need 15 years from now?

is the PV of ksh 500000 per year(ordinary annuity)for 15 yrs. At the above 10% p.a.+PV of the single sum of Ksh.1000000 at end yr. 75

ie. (500000*(1-1.10^-15)/0.10)+(1000000/1.10^15)=

4042431.803

ii. Amt.(Ksh.)Kiprono should save each year for the next 15 years to be able to meet his investment objectives as shown in i. ---assuming savings occurring at the end of each year----- is--

Given that he expects his salary to increase at the rate of 12 percent per year until his retirement--- ie. Growing annuity

So,using the Future value of growing annuity formula,

FV(GA)=(Pmt.(1+r)^n-(1+g)^n)/(r-g)

FV(GA)= the reqd. amt. found in i. above---ie. 4042432

Pmt.=the 1st payment---to be found out----??

r= the interest arte, 10%

g= the growth rate of the salary, 12%

n= no.of payment periods, ie. 15

So,

4042432=(Pmt.(1+10%)^15-(1+12%)^15)/(10%-12%)

Pmt.=4042432/((1+10%)^15-(1+12%)^15)/(10%-12%))

62367.93

iii. Suppose Kiprono wants to donate Ksh. 200,000 per year in the last 3 years of his life to a charitable cause.

Each donation would be made at the beginning of the year ie. At the end of his yrs. 57, 58 & 59--ie. At end of yrs. 12, 13 & 14 from now.

Money would he need when he reaches the age of 60

To meet this specific need alone, he will need

Sum of the 3 PV s at 10% per year

(200000/1.10^12)+(200000/1.10^13)+(200000/1.10^14)=

174325.29

iv.present value of his lifetime salary, if the discount rate is 8 percent?

is the PV of growing annuity, ie.

PV(GA)=(Pmt./(r-g))*(1-((1+g)/(1+r))^n)

ie.(400000/(8%-12%))*(1-(1.12/1.08)^15)=

7254962

(Answer)