Question

You’ve just joined the investment banking firm of Dewey, Cheatum, and Howe. They’ve offered you two different salary arrangements. You can have $6,100 per month for the next two years, or you can have $5,100 per month for the next two years, along with a $25,000 signing bonus today. Assume the interest rate is 7 percent compounded monthly. a. If you take the first option, $6,100 per month for two years, what is the present value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the present value of the second option? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

FIRST OPTION : PV = $136,244.11

SECOND OPTION : PV = $138,909.01

Explanation:

Given the following :

Option 1:

Annuity value(A) = $6,100

Period(n) = 2 years = 24months

Rate(r) = 7%=0.07

Monthly rate = 0.07÷12

Using the Present Value(PV) formula:

PV = A × [(1 - (1 + r) ^-n) ÷ r]

PV = $6100 × [ (1 - (1 + 7/12)^-24) ÷ 7/12]

PV = 136244.10625648

PV = $136,244.11

Second option:

Signing bonus = $25,000

Annuity value(A) = $5,100

Period(n) = 2 years = 24months

Rate(r) = 7%=0.07

Monthly rate = 0.07÷12

Using the Present Value(PV) formula :

PV = A × [(1 - (1 + r) ^-n) ÷ r]

PV = $5100 × [ (1 - (1 + 7/12)^-24) ÷ 7/12]

PV = $113909.00687017

PV = $113,909.01

Total PV = $(25,000 + 113,909.01)

= $138,909.01

Answer 2

Answer:

a. 1st option

No. of periods = 2*12 = 24 months

Annual interest rate = 7%, compounded monthly

so, monthly interest rate = rm = 7%/12

This is an annuity with a cash flow of $6100 per month for 24 months

C = 6100, no. of periods = n = 24, monthly rate = rm = 7%/12 = 0.00583333333333333

The  value of present annuity can be find out using the given formula:

PVAnnuity = (C/rm)*[1-(1+rm)-n]

PVAnnuity = (6100/(7%/12)) * [1-(1+(7%/12))-24]

PVAnnuity = 1045714.28571429*0.130288079225785 = 136244.105704678

Answer -> Present value of first option = $136244.11

b. 2nd option

In 2nd option, there is an amount that is paid today and also, there is an annuity, with monthly cash flow of $5100 for 24 months. Current value of this option will be the sum of C0 and the current value of the annuity .

Amount paid today as signing bonus = C0 = $25000

Annuity -> C = 5100, rm = 7%/12, n = 24

PVannuity = (5100/(7%/12))*[1-(1+(7%/12))-24] = 874285.714285714*0.130288079225785 = 113909.006408829

The current value of the 2nd option = C0 + PVAnnuity = 25000 + 113909.006408829 = 138909.006408829

Answer -> Present value of the 2nd option = $138909.01

Explanation: