Question

The Asset Privatization Trust had put up for sale a machine tools manufacturing plant. There were 2 bidders with the following proposals: (1) Bidder "A" offered P10M, payable 20% down payment, the balance payable P1M annually for 8 years. (2) O Bidder "B" offered P9M, payable P2 M down payment, the balance payable P0.5M semi-annually for 7 years. Which bid is more beneficial to APT and by how much is the difference if money is worth 10% effective? Show by

Answer 1

We need to calculate the present values of both proposals in order to find out a more beneficial one.

As both bidders are ready to pay down payment and equal annuities, we can use the present value of annuities formula to find out the present value of installments.

PV = PMT * (1-(1/(1+rⁿ)/r)

Where PV is the total present value of annuities

PMT = Annuity amount

r = Interest or discount rate

n = No. of payments

Bidder A

Present value of Down Payment(20% of Total Bid) = P2,000,000

The present value of eight annuities of P1,000,000

= 1,000,000 * (1-(1/(1+0.10⁸))/0.10

=1,000,000*(1-(1/2.143589))/0.10

=1,000,000*(1-(0.466507))/0.10

=1,000,000*0.533493/0.10

=1,000,000*5.334926

= P 5,334,926

Total Present Value of proposal 1 = P2,000,000 + P5,334,926 = P7,334,926

Bidder 2

Present value of Down Payment = P2,000,000

The present value of Fourteen annuities of P500,000 paid semi annually, means paid in 14 payments.

Here r = 0.10/2 = 0.05 for semi annual period

n = 14

= 500,000 * (1-(1/(1+0.05¹⁴))/0.05

= 500,000 * (1-(1/1.97993)/0.05

= 500,000 * (1-0.505068)/0.05

= 500,000 * 0.494932/0.05

= 500,000 * 9.898641

= P4,949,320

Total Present Value of proposal 2 = P2,000,000 + P4,949,320 = P6,949,320

Bidder A's proposal exceeds Bidder B's proposal by P385,606 (P7,334,926 - P6,949,320) and Bid A is more beneficial to APT.

Present Values of Annuities can also arrive by using the PV function in Excel.

Bidder A:

=PV(10%,8,-1000000,0,0)

=

P5,334,926.20

Add to this Down payment of P2,000,000 to arrive at total value.

Bidder B:

=PV(10%/2,14,-500000,0,0)

P4,949,320.47

Add to this Down payment of P2,000,000 to arrive at the total value.