Question

Calculate the number of ads per year to break even between two alterantives costs while considering the time-value of money.

An on-line commercial directory service must decide between composing the ads for its clients in-house or paying a production company to compose them. To develop the ads in-house, the company will have to purchase computers, printers, and a database management system at an estimated cost of $40,500. This equipment will have a useful life of 3 years, after which it will be sold for $4,300. The employee who creates the ads will be paid $59,000 per year. In addition, each ad will have an average cost of $15. Alternatively, the company can outsource development at a flat fee of $21 per ad. At an interest rate of 12% per year, how many ads must the company sell each year for the options to just break even?

The number of ads the company must sell for the options to just break even is determined to be

Answer 1

Let number of ads produced per year be X

Option : Develop ads in-house

Initial Cost=Co=$40500

Salvage value=S=$4300

Useful life=n=3 years

Rate of interest=i=12%

Salary per year=W=59000

Annual production cost=15X

Total annual Cost=(59000+15X)

PW of cost of option=-Co-R*(P/A,12%,3)+S*(P/F,12%,3)

PW of cost of option=-40500-(59000+15X)*(P/A,12%,3)+4300*(P/F,12%,3)

Let us calculate interest factors

(P/F,10%,3)=1/(1+12%)^3=0.711780

$(P/A,i,n)=\frac{1-\frac{1}{(1+i)^{n}}}{i}$

$(P/A,0.10,3)=\frac{1-\frac{1}{(1+0.12)^{3}}}{0.12}= 2.401831$

PW of cost of option=-40500-(59000+15X)*2.401831+4300*0.711780

PW of cost of option=-40500-141708.03-36.02747X+3060.654=-179147.376-36.02747X

Option : Outsource

Fee per ad=$21

PW of costs=-21*X*(P/A,102%,3)=-21*X*2.401831=-50.438451X

Set PW of both options equal

-179147.376-36.02747X=-50.438451X

X=179147.376/(-36.02747+50.438451)=12431.31

Number of ads should be 12431 per year to break even