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 $86,000 now and $62,000 in each of the next 6 years to improve productivity. By how much must annual costs decrease in years 7 through 13 to recover the investment plus a return of 9% per year?

The annual cost decreases by $  .

Answer 1

From years 7th to 13th, there are a total of 7 years.

We need to find the FV or the costs incurred from years 0-6 at the end of year 6 and then find the equal annual inflow that should be generated to recover this NPV

FV is calculated below:

Year	CF	Compounding t Factor		Compounded CF
0	$     86,000.00	(1+0.09)^(6-0)=	1.677100111	1.677100110841*86000=	$ 1,44,230.61
1	$     62,000.00	(1+0.09)^(6-1)=	1.538623955	1.5386239549*62000=	$     95,394.69
2	$     62,000.00	(1+0.09)^(6-2)=	1.41158161	1.41158161*62000=	$     87,518.06
3	$     62,000.00	(1+0.09)^(6-3)=	1.295029	1.295029*62000=	$     80,291.80
4	$     62,000.00	(1+0.09)^(6-4)=	1.1881	1.1881*62000=	$     73,662.20
5	$     62,000.00	(1+0.09)^(6-5)=	1.09	1.09*62000=	$     67,580.00
6	$     62,000.00	(1+0.09)^(6-6)=	1	1*62000=	$     62,000.00
				FV = Sum of all Discounted CF	$ 6,10,677.35

Now to find the annual inflow we use the below formula

Verifying the same we can draw the below PV schedule:

Year	CF	Discount Factor		Discounted CF
0	$   -86,000.00	1/(1+0.09)^0=	1	1*-86000=	-86,000.00
1	$   -62,000.00	1/(1+0.09)^1=	0.917431193	0.91743119266055*-62000=	-56,880.73
2	$   -62,000.00	1/(1+0.09)^2=	0.841679993	0.84167999326656*-62000=	-52,184.16
3	$   -62,000.00	1/(1+0.09)^3=	0.77218348	0.772183480061064*-62000=	-47,875.38
4	$   -62,000.00	1/(1+0.09)^4=	0.708425211	0.708425211065196*-62000=	-43,922.36
5	$   -62,000.00	1/(1+0.09)^5=	0.649931386	0.649931386298345*-62000=	-40,295.75
6	$   -62,000.00	1/(1+0.09)^6=	0.596267327	0.596267326879216*-62000=	-36,968.57
7	$ 1,21,335.80	1/(1+0.09)^7=	0.547034245	0.547034244843317*121335.798797947=	66,374.84
8	$ 1,21,335.80	1/(1+0.09)^8=	0.50186628	0.501866279672768*121335.798797947=	60,894.35
9	$ 1,21,335.80	1/(1+0.09)^9=	0.46042778	0.460427779516301*121335.798797947=	55,866.37
10	$ 1,21,335.80	1/(1+0.09)^10=	0.422410807	0.422410806895689*121335.798797947=	51,253.55
11	$ 1,21,335.80	1/(1+0.09)^11=	0.38753285	0.387532850363017*121335.798797947=	47,021.61
12	$ 1,21,335.80	1/(1+0.09)^12=	0.355534725	0.355534725103686*121335.798797947=	43,139.09
13	$ 1,21,335.80	1/(1+0.09)^13=	0.326178647	0.326178646884115*121335.798797947=	39,577.15
				NPV = Sum of all Discounted CF	0.00

As NPV = 0, our calculations are correct.