Answer to Question #108538 in Financial Math for Suvi

Question

An investor is considering purchasing an office block.

Rental income will be received continuously for 40 years starting at £80,000 per annum. Rents are increased every 4 years at a rate of 3% per annum compound, with the first increase taking place 4 years after purchase.

The investor estimates that £300,000 will need to be spent to refurbish the building 9 months after the purchase date.

The shops are also expected to require regular refurbishment every 4 years for 36 years, with the first such refurbishment taking place at time t = 4 years at an initial cost of £20,000. These regular refurbishment costs are also expected to increase by 3% per annum compound.

The property reverts to its original owner after 40 years for no payment.

Assuming that the investor requires an internal rate of return of 10% per annum and pays no tax, calculate the price that the investor would be willing to pay.

Answer 1

1. find the strength of growth and income in 40 years

$\sigma=ln(1+r)=ln(1+0.03)=0.02956$

$S=P\times e^{\sigma n}=times 3200 000\times e^{0.2956}=4 300 480$

1. find the strength of growth and costs in 36 years:

$\sigma=ln(1+r)=ln(1+0.03)=0.02956$

$C=P\times e^{\sigma n}=times 720 000\times e^{0.26604}=939 441.6$

Ct=300 000+939 441.6=1 239 441.60

1. find the originally invested funds

$0=\frac{4 300 480-1 239 441.6}{(1+0.1)^{40}}-IC$

IC=67632.31