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:
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
