# BUS 1003H - Tutorial 17: Question 4

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The question from the tut is as follows:

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answered Oct 26, 2016 by (4,010 points)

To calculate the price which the insurer is prepared to pay we need to find the present value of all the inflows and outflows.

Firstly the PV for the sale of the property:

$$PV(sale) = 900 000 000 \times V^{30}_{i=12} = 30040131.49$$

Secondly, for the PV for the expenses we use an increasing annuity. As the first payment of 2 million is only due in a years time we need to decrease it by six per cent so that the increases and Vs will have the same powers, allowing for the use of the annuity in arrears formula:

$$PV(expenses) = \frac{2000000}{1.06} \times a_{\bar{30|} j} = 26943139.63$$

where $$j = \frac{1.12}{1.06} - 1 = 0.0566$$

Finally for the PV of the rent we can handle it in two stages treating the first five years and the remaining 25 years differently. This is due to the 90% occupation which occurs after the first five years and because of the 7% increases which happens at the end of the first fives years. The PV for the first five years can be found as:

$$PV(inc_{5y}) = 12 \times 1250000 \times \ddot{a}_{\bar{5|} l} = 72368834$$

where $$l = \frac{1.12}{1.1} - 1 = 0.18$$

The PV for the next twenty five years can be found as:

$$PV(inc_{25y}) = V^5 \times 0.9 \times 12 \times 1250000(1.1)^5 \times \ddot{a}_{\bar{25|} k} = 188120735$$

where $$k = \frac{1.12}{1.07} - 1 = 0.467$$

The final price is then:

$$Price = PV(inc_{5y}) + PV(inc_{25y}) + PV(sale) - PV(expenses) = 263586562$$