Question

In: Finance

Two payment plans are considered. Plan A pays $100 immediately, $200 in 2 years and $100...

Two payment plans are considered. Plan A pays $100 immediately, $200 in 2 years and $100 in 3 years. Plan B simply pays $350 immediately.

(a) Compare the present values of Plan A and Plan B at 7.8% and 8.5% effective interest rate per year.

(b) Assume Plan A is purchased for $350 at the time of the first payment.

Prove the existence of a unique yield rate which lies between 7.8% and 8.5%.

(c) Using a single iteration of linear interpolation between 7.8% and 8.5%, find an approximate yield rate.

Solutions

Expert Solution

Ans (a)

Plan A
Year 0 1 2 3 Total
Cash flow 100 0 200 100
PV Factor @7.8% 1 0.9276 0.8605 0.7983
PV Factor @8.5% 1 0.9217 0.8495 0.7829
PV @ 7.8% 100 0 172.1 79.83 351.93
PV @ 8.5% 100 0 169.9 78.29 348.19

Plan B simply pays $350 immediately, so its present value is $350.

Plan Discount Rate Present Value
A 7.80% 351.93
B 7.80% 350
Plan Discount Rate Present Value
A 8.50% 348.19
B 8.50% 350

Ans (b)

Ans (c)

jeff jeffy answered 1 year ago
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