FIN534 Week 4 Homework
1. What is the present value of the following uneven cash flow stream − $50, $100, $75, and $50 at the end of Years 0 through 3? The appropriate interest rate is 10%, compounded annually
Years 0 1 2 3
$50 100 75 50
In case of uneven cash flow present value formula used will be the same as that of single cash flow. Thus we consider each value as a single cash flow calculate their present value and add them all to calculate the total present value. Zero year in the cash flow stream means today so amount of $50 today will remain $50 and we will discount the remaining amounts i.e. 100, 75 and 50 to calculate their worth today.
Formula to calculate PV of single cash flow is PV=fv/ (1+i) n
PV = $50 + 100/ (1+.1)1+ 75/ (1+.1)2 + 50/ (1+.1)3
50+ 90.909 + 61.98 + 37.56
2. We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company’s sales are growing at a rate of 20% per year, how long will it take sales to double.
In this case we will use 72 rule that is being used to calculate the interest rate required to double the amount if number of years are given or vice versa. The formula of 72 Rule is as follow
72 = n*i
72 = n * 20
N = 72/20
N= 3.6 years.
3. Will the future value be larger or smaller if we...