Question

you are a freelancer and were offered two gigs. one will pay you $25,000today and the other will pay you $5,000 per year over the next six years. assuming your required return is 8%, which gig should you accept, assuming you are in it just for the money?

Answer 1

The preferred gig is the first one since its today's worth is greater than the today's value of the second gig

What is the today's worth of $5000 each year?

The worth of the second gig, which pays $5000 every year for the next 6 years in today's dollar is the present value of all the six annual cash flows discounted using the present value formula of an ordinary annuity as shown below:

PV=PMT*(1-(1+r)^-N/r

PV=present value of annual payments for 6 years=unknown

PMT=annual payment=$5000

r=required return=discount rate=8%

N=number of annual cash flows=6

PV=$5000*(1-(1+8%)^-6/8%

PV=$5000*(1-(1.08)^-6/0.08

PV=$5000*(1-0.630169626883105)/0.08

PV=$5000*0.369830373116895

/0.08

PV=$23,114.40

The fact that the present value of the second option which pays $5000 annually is lesser than the amount receivable immediately, which is $25,000, hence, the first gig is preferred

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