A group of nerds perfect a process for converting seawater into crude oil. In or

Question

A group of nerds perfect a process for converting seawater into crude oil. In order to keep their process off the market, OPEC offers license to process by paying the nerds an annual royalty payment of $100,000,000 starting one year from now, and then increasingly annyally there after at a 4% rate forever. The nerds have figured out that they won't live forever, and they decide to sell their royalty rights to J.G. Spentworth Financial for a one-time lump sum payment based on a 10% discount rate their financial advisor recommended. What price, in whole dollars, should they expect to receive if J.G. Spentworth meets their expectations?

**Answer is $1,666,666,667, but have no idea how to solve** Please show all work and calculator functions if possible.

Explanation / Answer

Let c=100,000,000 be the pay 1 year from now and that the pay thereafter grows at rate g=4% forever so that pay in second year is c(1+g), in third year of c(1+g)2,so on till infinity. The present value of whole of this future pays is given by discounting future pays at rate of r=10%.

PV=c/(1+r)1+ c(1+g)/(1+r)2+c(1+g)2/(1+r)3+...........inf

PV=c/(1+r)1[ 1+(1+g)/(1+r)1+(1+g)2/(1+r)2+...........inf]

1+(1+g)/(1+r)1+(1+g)2/(1+r)2+...........inf is an infinite GP with first term=1 ,common ratio=cr=(1+g)/(1+r) and

sum=first term/(1-cr)=1/(1-(1+g)/(1+r))=1/((1+r)-(1+g)/(1+r))=(1+r)/(r-g)

Thus PV=c/(1+r)[ (1+r)/(r-g)] = c/(r-g)

PV= 100,000,000/(.10-.04)=100,000,000/.06=1666666666.667=~$1,666,666,667

Thus they expect to receive $1,666,666,667 if J.G. Spentworth meets their expectations.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.