Question

(Related to Checkpoint 5.4) (Present-value comparison) You are offered $110,000 today or $360,000 in 14 years. Assuming that you can earn 12 percent on your money, which should you choose? If you are offered $360,000 in 14 years and you can earn 12 percent on your money, what is the present value of $360,000? (Round to the nearest cent.)

Answer 1

Offered today = $110,000

Offered in 14 years = $360,000

Interest rate = 12%

Present Value of $360,000 offered in 14 years at 12% = $360,000* Discount Factor at 12% for 14th year

=$360,000*(1/(1+12%)^14) = $360,000*0.20462 = $73,663.20

Present Value of $360,000 in 14 years = $73,663.20

Since the offer today of $110,000 is higher than present value of $360,000 in 14 years of $73,663.20, today's offer of $110,000 needs to be accepted.

Answer 2

SOLUTION :

It requires to compare the present values of options to select the better one. Higher the PV, better is the option. 

Accordingly, we determine PVs of the two options .

Option 1 :

$110000 today .

Its PV = $110000 .

Option 2 :

Receiving $360000 in 14 years from now. 

Required rate, r = 12% = 0.12

=> 1 + r = 1.12

PV of Option 2 

= FV/(1 + r)^n 

= 360000 / 1.12^14 

= 73663.13 ($) 

PV of Option 2 is = $73663.13(ANSWER)

So, PV of Option 1 is higher than that of Option 2. 

Hence, Option 1 should be accepted. (ANSWER).