Question

Donna and Keith want to sell their business. They have received two offers. If they accept Offer A, they will receive $61,000 immediately and $20,000 in three years. If they accept Offer B, they will receive $37,000 now and $3,000 at the end of every six months for 5 years with the first payment received 6 months from now. If interest is 6.67% annually, which offer is preferable for Donna and Keith? Give proper explanation with formula, not answer solved with software.

Answer 1

By compare these offers by thier present value of both offers

Offer A is $61,000 received today and 20,000 received in year 3.

Present value of Offer A = 61,000 + 20,000 *PVF(6.67%,3 years)

PVF Formula = 1 / (1+i)n = 1/(1+6.67%)3

= 61,000 + 20,000 * 1/(1.0667)3

= 61,000 + 20,000 * 0.823897

= 61,000 + 16,477.9473

present value of offer A =$ 77,477.9473

Offer B is $ 37,000 received today and 3000 received at end of every six years for 5 years.

Present value of Offer B = 37,000 + 3000 * present value of annuity factor for 5 year at 3%

= 37,000 + 3000 * { 1 - 1/(1+i)n } / i

Here n = number of semi annual pauments = 5 years * 2 = 10 payments

i = annual interest rate

= 37,000 + 3000 * { 1 - 1/(1.0667)10} / 0.0667

= 37,000 + 3000 * 0.475703 / 0.0667

= 37,000 + 3000 * 7.131985

= 37,000 + 21,395.9546

Present value of offer B= $ 58,395.9546

Here Present value of offer A ( $ 77,477.95) is higher than present value of offer B (58,395.546)

So,Offer A is Preferable.