Question

As an innovative way to pay for various software packages, a new high-tech service company
has offered to pay your company, Custom Computer Services (CCS), in one of two ways: (1)
pay $500,000 now, (2) pay $1.4 million 5 years from now.
a) If the real interest rate is 14% per year and the inflation rate is 10% per year, which offer
should you accept? (15 points)
b) If your company was offered to be paid an amount of money 5 years from now that will
have the same purchasing power as $850,000 now, would this change your decision resulted
in part (a) of the question. (consider the same interest and inflation rates given in part a).
(10 points)

Answer 1

a)

The formula for inflated rate as follows:
ir= i+f+if
= 0.14+0.10+0.14×0.10
= 0.254 or 25.4%
Where i= interest rate
f= inflation rate
ir=inflated rate

Option 1= pay $500000 now
Option 2= pay $1.4 million 5 years from now

Formula :
FV= PV×(1+ir)^n
Where FV= future value
PV= Present value
n= no of years
ir= inflated rate

Hence, to calculate the PV of $1.4 million dollars:
1400000=PV×(1+25.4%)^5
1400000=PV×3.1008194391
1400000/3.1008194391= PV
Hence, PV= $ 451494 ( Approx)

So, on comparing both options clearly we can say CCS will choose option 1 because in option 1 we receive 500000$ but in option 2, CCS will receive only $451494 as on today.
Hence CCS should go for Option 1.

b)
If company was offered to be paid an amount of money 5 years from now that will have the same purchasing power as $850,000 now, this will definitely change our decision because on comparing
Present value of both option 1 i.e $500000 now and the option given in b), we can say that the purchasing power of 850000$ as on today is obviously more than 500000$ today.
Also, we can compare FV of both the options.
Option 1: 500000$ today
FV= PV×(1+ir)^n
FV= 500000×(1+25.4%)^5
FV= 1,550,410 $

Option 2: 850000$ today
FV= PV×(1+ir)^n
FV= 850000×(1+25.4%)^5
FV= 2,635,696$

CCS decision will change and will go for option 2.