Question

There are 4 different ways to pay for your property recently purchased. The four options stated below:

1. $ 200,000 p.a. paid every year for 5 years. the first payment paid at the end of the first year.

2. $250,000 p.a. for 6 years. first payment paid at the end of the first year.

3. $1,000,000 at the end of the 5th year and $1,250,000 at the end of the 10^th year.

4. A $20,000 deposit paid immediately & $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.

If the rate of return is 12 percent per annum, list the 4 options from cheapest to most expensive. Also state the PV of each alternative.

Answer 1

i. PV is computed as follows:

Present value = Annual payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 200,000 x [ (1 - 1 / (1 + 0.12)⁵ ) / 0.12 ]

= $ 200,000 x 3.604776202

= $ 720,955.24

ii. PV is computed as follows:

Present value = Annual payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 250,000 x [ (1 - 1 / (1 + 0.12)⁶ ) / 0.12 ]

= $ 250,000 x 4.111407324

= $ 1,027,851.83

iii. The PV will be as follows:

= Future value / (1 + r)ⁿ

= $ 1,000,000 / 1.12⁵ + $ 1,250,000 / 1.12¹⁰

= $ 969,893.40

iv. The present value will be as follows:

= Amount paid immediately + Amount paid in 1 year / (1 + r)

= $ 20,000 + $ 100,000 / 0.12

= $ 853,333.33

So, the options from cheapest to expensive will be as follows:

Option i, Option iv, Option iii and Option ii.