Question

P5-49 Growth rates You are given the series of cash flows shown in the following table, Cash flows Year ABC R500 R1,500 R2,500 2 560 1.550 2,600 640 1.610 2,650 720 1.680 2,650 1.760 2,800 1,850 2.850 1.950 2.900 2,060 2.170 2.280 800 a. Calculate the compound annual growth rate associated with each cash flow stream. b. If year-1 values represent initial deposits in a savings account paying annual interest, what is the annual rate of interest earned on each account? C. Compare and discuss the growth rate and interest rate found in parts a and b, respectively

Answer 1

Solution:

Part A )

CAGR Coumpound annual growth rate that can be calculated by using this formula

CAGR = (Final / initial ) ^ (1/n) -1

For cash flow A , CAGR = (800/500)^(1/4) -1 = 1.124683-1 = .124683= 12.46%

For cash flow B ,

CAGR = (2280/1500)^(1/9) - 1 = 1.072278-1 = 7.23%  

For cash flow C,

CAGR = (2900/2250)^ ( 1/6) -1 = 1.043204-1 = 4.32%

Part B )

It is given that 1st Year deposit is in saving bank and we need to find the interest rate

Cash flow A

Interest earned = final amount - invested amount = 800-500 = 300

Year = 4

We can calculate the simple interest rate for this period

Interest rate = 300/(500*4 ) = 15%

Similarly for cash flow B

Interest earned = 2280-1500 = 780

Interest rate = 780/ ( 1500*9) = 5.78%

For cash flow C

Interest earned = 2900-2250 = 650

Interest rate= 650 / ( 2250*6) = 4.81%

Part C )

Growth rate is lower than the interest rate if we consider simple interest rate for saving account and it will be similar if we take into the consideration of compound interest