Question

Dora Nyika is a student pursuing a Bachelor’s Degree in Business Studies (BBS) at a certain University in Zambia. Dora will graduate in one year’ time and has applied for a job with an international telecommunication company. As part of the company’s evaluation process, she has been asked to take an examination which covers several time value of money concepts and principles. Dora has been asked to provide answers to the following questions: (a) To draw time lines for: (i) An uneven cash flow stream of K500, -K700, K850 and K200 at the end of years 0 to year 3 (ii) A K50,000 lump sum cash flow at the end of year 3. (iii) An ordinary annuity of K5,000 per year for 3 years (b) How long it will take a sum of money of money (or anything else) to grow to some specified amount. For example, if a company’s production is growing at a rate of 15% per year, how long will it take production to double? Say we want to find out how long it will take us to double our money at an interest rate of 15%. Note: do not use the rule of 72 when answering this question (c) If you want an investment to double in 4 years, what interest rate must it earn? (d) What is the future value of a 5-year ordinary annuity of K2,000 if the appropriate rate of return is 8%? (e) What is the present value of the ordinary annuity? (f) What would be the future and present values if the annuity were an annuity due? Instructions: Answer the above questions on behalf of Dora Nyika and present the work in a report format.

Answer 1

Answer 1 )

Draw Time lines for the Cash Flows

YEARS	Cash Flows	Annuities	Lump Sum	Total Cash Flows
0	500	5,000		5,500
1	(700)	5,000		4,300
2	850	5,000		5,850
3	200	5,000	50,000	55,200

Answer 2)

How long will it take to double at 15% interest rate

We want to calculate the number of years

PV = FV * (1+int%)^n

55,200 = 110,400 * (1.15) ^n

n = 5 years (4.95 exact value)

Answer 3)

If we want interest rate to double in 4 years, what interest must be earned

PV = FV * (1+int%)^n

55,200 = 110,400 *( 1+int%) ^ 4

int.% = 18.92%

Answer 4)

FV of 5 year ordinary annuity of 2,000 if rate of return is 8%

FV = PMT1 * (1=int%) ^n + PMT2 * (1=int%) ^n-1 + PMT3 * (1=int%) ^n-2 +.... PMT4 * (1=int%) ^n-4

or using FV funtion in excel or Financial calculator input the following values:

N = 5

PMT = 2000

PV = 0

I/Y (Rate) = 8%

FV = 11,733.20