Laura is the management accountant for the leisure centre and she has been asked to evaluate the alternative proposals.

Proposals

$($i$)$ Alternative $1-$ Incorporate squash court No$.4$

Increase the size of the fitness room by incorporating squash court $4.$ This would increase the size of the fitness room from $2,200$ sq$.$ ft to $2,700$ sq$.$ ft$.$

Squash court $3$ would remain and it would be refurbished immediately.

$($ii$)$ Alternative $2$ Incorporate squash courts $3$ and $4$

Increase the size of the fitness room by incorporating squash courts $3$ and $4.$ This would increase the size of the fitness room from $2,200$ sq$.$ ft to $3,200$ sq$.$ ft$.$

Capital costs

The capital costs of the alternatives include building works, services, equipment, and professional fees. Estimates are given below:

Building works

Alternative $1$ $$15,600$

Alternative $2$ $$22,100$

Services

Alternative $1$ $$20,000$

Alternative $2$ $$20,900$

Equipment

Alternative $1$ $$46,100$

Alternative $2$ $$86,900$

A residual figure at the end of $6$ years was estimated at $6,000$ for alternative $1$ and $9,000$ for alternative $2.$

Professional fees and charges $$6,000$

Annual costs

Alternative $1$ $$38,700$

Alternative $2$ $$47,100$

The cost of advertising the new facilities at the leisure centre is estimated at $$15,000$ in the first year. June believed an aggressive advertising policy was essential to ensure the project was a success. No estimate for advertising was considered for later years.

Estimating additional annual revenue for fitness room $($two different approaches are to be considered$)$

June

She has suggested that additional revenue should be estimated by dividing the current income of $$180,000$ by $2,200$ sq$.$ ft to determine income per sq$.$ ft$.$ The income per sq$.$ ft$.$ is assumed to remain constant as the size of the fitness room is increased. Basing income on square footage is seen as a simple but accurate way of estimating future income.

Laura

Laura suggested a different approach. She suggested that managers should use a probability distribution based on the judgement of all the senior managers to estimate the total revenue for the fitness room. After much discussion Laura was able to suggest the following probability distribution:

Alternative $1$

State of World Total annual revenue for the fitness room. Probability $\%$

I $-$ The fitness room will be an initial success but too few new members will be attracted. Usage will vary throughout the year. $$210,00020\%$

II $-$ The fitness room will be very successful initially but then membership will slowly fall. Usage will be seasonal. $$225,00050\%$

III $-$ The fitness room will be very successful. A lot of new members will be attracted and as existing members become more health conscious they will use the room throughout the year. $$250,00030\%$

Alternative $2$

State of World Total annual revenue for the fitness room. Probability $\%$

I $-$ The fitness room will be an initial success but too few new members will be attracted. Usage will vary throughout the year. $$240,00050\%$

II $-$ The fitness room will be very successful initially but then membership will slowly fall. Usage will be seasonal. $$250,00040\%$

III $-$ The fitness room will be very successful. A lot of new members will be attracted and as existing members become more health conscious they will use the room throughout the year. $$270,00010\%$

$($The additional revenue equals the total revenue calculated above less the existing revenue of $$180,000).$

Cost of capital

Laura suggests that it is appropriate to use a cost of capital of $7\%$ for this project.

Other related information from Laura

Laura wants the following information to be considered.

$(1)$ Both squash courts $3$ and $4$ are in urgent need of refurbishment. It has been agreed that if one court is going to be used in the future it will be refurbished immediately at a cost of $$10,000.$

If both courts are going to be used in the future they will be refurbished immediately at a cost of $$25,500.$

$(2)$ If one court is closed the total income from the squash courts will fall by $$10,000$ per annum.

If two courts are closed the total income from the squash courts will fall by $$15,000$ per annum.

$($These estimates are based on last year$$s booking information$)$

$(3)$ The restaurant manager expects to see more customers if the fitness room is increased in size.

If the fitness room is increased in size by closing one court the restaurant manager estimates his profits will increase by $$17,000$ per annum.

If the fitness room is increased in size by closing two courts the restaurant manager estimates his profits will increase by $$23,800$ per annum.

Question $1$

$($i$)$ Evaluate the sensitivity of the investments and make a clear recommendation on financial grounds to accept or reject the investments.