Question

You have bought a property and have four different options on how to pay for the property purchase. The four options are:

1. $ 200,000 p.a. paid every year for five years with the first payment paid at the end of the first year.

2. $250,000 p.a. for six years with the first payment paid at the end of the first year.

3. $1,000,000 at the end of the fifth year and $1,250,000 at the end of the 10^th year.

4. A $20,000 deposit paid now plus $100,000 p.a. paid forever from the rental of the property. The first $100,000 is paid at the end of the first year.

Required:

Using a required rate of return of 12% p.a., rank the order in which you would pay for the property from cheapest to most expensive, and provide the PV of each option.

Answer 1

Option i:

P = Annual payment = $200,000

n = 5 years

r = required rate of return = 12%

Present Value of the option = P * [1 - (1+r)^-n] / r

= $200,000 * [1 - (1+12%)^-5] / 12%

= $200,000 * 0.432573144 / 0.12

= $720,955.2405

= $720,955.24

Option ii:

P = Annual payment = $250,000

n = 6 years

r = required rate of return = 12%

Present Value of the option = P * [1 - (1+r)^-n] / r

= $250,000 * [1 - (1+12%)^-6] / 12%

= $250,000 * 0.493368879 / 0.12

= $1,027,851.831

= $1,027,851.83

Option iii:

Present Value of Option = [$1,000,000 / (1+12%)^5] + [$1,250,000 / (1+12%)^10]

= [$1,000,000 / 1.762341683] + [$1,250,000 / 3.105848208]

= $567,426.8557 + $402,466.5457

= $969,893.4015

= $969,893.40

Option iv:

Present Value of Option = $20,000 + [$100,000 / 12%]

= $20,000 + $833,333.3333

= $853,333.333

= $853,333.33

The Expensive to Cheapest order is as below

Present Value of Option ii is $1,027,851.83

Presnt Value of Option iii is $969,893.40

Present Value of Option iv is $853,333.33

Present Value of Option i is $720,955.24

Therefore, Option i should be selected