A local university has decided to embark on a project to invest in a new buildin
ID: 2791255 • Letter: A
Question
A local university has decided to embark on a project to invest in a new building The building will provide accommodation and teaching facilities for 300 extra students. The building provides the following costs and benefits Costs Initial building costs of £11,700,000 + £9,000x which are spread evenly and continuously over the period from 1 January 2018 to 1 July 2019. Extra staff and maintenance costs of £500,000 per annum incurred annually in advance for 10 years from 1 January 2020 . Benefits Rent from each student payable monthly in advance for 10 years from 1 January 2020. The monthly rent is £400 per student Extra tuition fees for each student payable annually in arrear for 10 years from 2020 i.e. the first fees are payable on 31 December 2020. The extra annual fees per student are £3,000 in 2020, £3,500 in 2021 and increase by £500 each year. . Calculate, using an effective interest rate of 12% per annum, the present value as at January 2018 of (i) the building costs (ii) the staff and maintenance costs (iii) the rental income (iv) the tuition fees Hence calculate the net present value as at 1 January 2018 for the project using an effective risk discount rate of 12% per annum and determine whether the project is worth undertaking a) b)Explanation / Answer
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P = Pounds = GBP = Great Britain Pounds, m = million
Costs
Investment 11,700,000 + 9,000 =
GBP 11,709,000.00
The initial cost of P 11.709 m spread for 18 months will give a monthly cost of
GBP 650,500.00
Annual Staff and Maintain cost per year
GBP 500,000.00
9878540.211
Benefits
Monthly rent
GBP 400.00
Annual rent = 400 * 12
GBP 4,800.00
Year
Tuition fees
GBP 3,000.00
2020
GBP 3,500.00
2021
GBP 4,000.00
2022
GBP 4,500.00
2023
GBP 5,000.00
2024
GBP 5,500.00
2025
GBP 6,000.00
2026
GBP 6,500.00
2027
GBP 7,000.00
2028
GBP 7,500.00
2029
GBP 52,500.00
Part a) interest rate i = 12% = 0.12
As of 1 JAN 2018:
a.i) Building costs per month
GBP 650,500.00
Present value of the building cost = 1.5 years into 11 million pounds
GBP 9,878,540.21
a.ii) Staff and Maintain costs
500,000 per annum for 10 years = 10*500,000 = 5 million
GBP 5,000,000.00
Present value of the 5 million =
PV
GBP 1,609,866.18
a.iii) income from rent
Annual rent = 400 * 12
GBP 4,800.00
Rent for 10 years = 4800 * 10 =
GBP 48,000.00
PV
GBP 15,454.72
a.iv) income from tuition
For all 10 years =
GBP 52,500.00
PV
GBP 16,903.59
Sum of all PVs =
GBP 1,642,224.49
Part b) Discount Rate = 12% = 0.12
Net Present Value (NPV) as at 1 jan 2018
GBP 1,642,224.49
Apply the risk discount rate of 12% on the total PV =
GBP 197,066.94
Subtracting the risk discount rate
GBP 1,445,157.55
Is it viable to do this project? Will it be a go or no go?
GO
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Discount rate adjusted for the Risk = Rate free of the risk + premium for the risk
But when we apply the Capital Assets Price Modeling (CPAM), then
Premium of the Risk = ( Rate of Return prevailing in the market at present - Rate free of risks ) * Project Beta
i = interest rate = 12 % = 0.12
n = number of terms, time or duration = 18 months = 1.5 years
Future Value = FV = P 11,709,000
a.i)
Present Value = PV =
FV = PV * ( 1 + i ) ^ n
PV = FV / ( (1+i) ^ n )
PV = 11709000 / ( ( 1+0.12)^1.5)
PV = GBP 9,878,540.211
So, approximately, 9 million pounds becomes 11 million in 18 months
a.ii)
PV = FV / ( (1+i) ^ n )
PV = 5000000/((1.12)^10)
= P 1.60986618 million
So this is also logical, P 1.61 million becomes P 5 million in 10 years
a.iii)
PV = 48000/(1.12^10)
= P 15,454.72
a.iv)
Tuition FV = P 52,500
PV = 52500/(1.12^10)
= GBP 16,903.59
So, when we go ahead with this college project we would have lost the interest income of 1,609,866.18 + 15,454.72 + 16,903.59 = GBP 1,642,224.49
If we could recover equal to or above this amount by using the discount rate then it is worth the effort
Part b)
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Costs
Investment 11,700,000 + 9,000 =
GBP 11,709,000.00
The initial cost of P 11.709 m spread for 18 months will give a monthly cost of
GBP 650,500.00
Annual Staff and Maintain cost per year
GBP 500,000.00
9878540.211
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