Hort is an actuarial consultancy. Hort has owned a two floor office block for the past20 years.

Improvements in technology mean that Hort has reached the point where the whole ofthe upper floor is left unoccupied.

Hort's directors are considering using the free space in the building to launch a newconsultancy venture. This would involve taking on new consultants with relevantexpertise, as well as equipping the floor with suitable IT equipment.

The initial investment in the IT equipment will be 1.5 million.

Over the next five years, Hort predicts that the fees earned from the new consultancyventure, minus the cash outflows associated with wages and other running costs, willhave a net present value of 4.0 million.

Hort's directors believe that they should allow something for the building in decidingwhether to proceed with this venture. Four possible arguments have been put forwardby four members of the board:

1. The building cost 2.0 million when it was acquired and it has been depreciatedby 800,000 since. That leaves a net book value of 1.2 million, of which 0.6million could be attributed to the upper floor.

2. The cost of the building is a sunk cost and it should not be incorporated into theproject appraisal.

3. The upper floor could be sold to a third party for 2.7 million.

4. The upper floor could be rented out over the next five years, with rental incomeyielding a net present value of 0.9 million.

The debate over the building has been heated because it could affect the decision togo ahead with the project.

(i) Discuss the logic of each of the four arguments concerning the building. [8]

(ii) Explain how Hort's Board should decide on the most appropriate treatment ofthe building. [2]

Critics of the net present value (NPV) technique state that it has a fundamental flaw inthat it is possible to justify either the acceptance or rejection of almost any project by

manipulating estimates and assumptions in the evaluation of NPV.

(iii) Evaluate the assertion that this project illustrates this fundamental flaw in thenet present value criterion. [10]

[Total 20]

In any year, the rate of interest on funds invested with a particular company has mean value / and standard deviation s, and is independent of the rates of interest in all previous years. (i) Derive formulae for the mean and the variance of the accumulated value after n years of a single investment of 1 at time 0. [5] (ii) Let i be the rate of interest earned in the /th year. Each year the value of (1 + i, ) is lognormally distributed, with parameters / = 0.04 and o- = 0.09. (a) Show that n, the number of years that must elapse before the accumulation of a lump sum invested at time 0 has a 75% probability of at least doubling in size, satisfies: 0.04n - 0.2024vn - In 2 =0 (b) Hence, or otherwise, calculate the value of n. [8] [Total 13]Three bonds paying annual coupons in arrears of 7% and redeemable at 105 per f100 nominal reach their redemption dates in exactly one, two and three years time, respectively. The price of each of the bonds is f98 per f100 nominal. (i) Determine the gross redemption yield of the 3-year bond. [3] (ii) Calculate all possible spot rates implied by the information given. [5] [Total 8]