Question

A recently hired chief executive officer wants to reduce future production costs to improve the company’s earnings, thereby increasing the value of the company’s stock. The plan is to invest $96,000 now and $54,000 in each of the next 4 years to improve productivity. By how much must annual costs decrease in years 5 through 13 to recover the investment plus a return of 12% per year?

Answer 1

Solution:

Future value of investment:

Future value of investment
Year	Cash flow	Future value factor	Future value
0	$96,000	1.5735	$151,056.00
1	$54,000	1.4049	$75,864.60
2	$54,000	1.2544	$67,737.60
3	$54,000	1.1200	$60,480.00
4	$54,000	1.0000	$54,000.00
			$409,138.20

Yearly savings required:

	Annuity payment	P/ [ [1- (1+r)-n ]/r ]
P=	Present value	$409,138.20
r=	Rate of interest per period
	Rate of interest per annum	12%
	Payments per year	1.00
	Rate of interest per period	12%
n=	number of payments:
	Number of years	9
	Payments per year	1.00
	number of payments	9
	Annuity payment=	$409,138.20/ [ (1- (1+0.12)^-9)/0.12 ]
	Annuity payment=	$2,179,990.53