Question

John Aitorea was seriously injured an individual in an industrial accident. He used the responsible parties and was awarded a judgement of $2 million dollars. Today, he and his attorney are attending a settlement conference with the defendants. The defendants have made an initial offer of $156,000 per year for 25 years. John plans to counteroffer at $255,000 per year for 25 years. Both the offer and the counteroffer have a present value of $2 million, the amount of judgment. Both assume payment =s at the end of the year
a. What interest rate assumption have the defendants used in their offer?
b. What interest rate assumption have john and his lawyer used in their counteroffer?
c. Suppose john is willing to settle for an annuity that carries an interest assumption of 9%. What annual payment would be acceptable to him?

Answer 1

a.Rate of interest assumption for defendant.

$$P(1+r)^n$$

$$156000(1+r)^n=2000000$$

$$(1+r)^{25}=12.82051282$$

$$1+r=1.10742982$$

$$r=0.10742982=10.742982\%$$

b.Interest rate for complainant

$$255000(1+r)^{25}=2000000$$

$$(1+r)^{25}=7.84317255$$

$$1+r=1.08580919$$

$$r=0.08580919=8.588019\%$$

c. Formula for annuity payments is

$$P={r(pv)\over1-(1+r)^{-n}}$$

$$P=\frac{\frac{9}{100}\cdot \,2000000}{1-(1+\frac{9}{100})^{-25}}$$

$$P=203612.50111$$