Tutorial 7 Flashcards
1) On 1 January 2010 and investor has the choice of two projects A and B with i = 10% pa (12).
Project A involves an initial cost of £10,000 and provides income in arrears of £900 at the
end of the first year, inflating at 5% pa, with the last payment being on 31 December 2014.
The investor will then be able to sell the ongoing rights to the project at 31 December 2014
after the last payment for £15,000.
Project B involves an initial cost of £10,000 provides an income on 31 December 2012 of
£2,500 and the investor will then be able to sell the ongoing rights to the project at 31
December 2014 for £18,000.
Calculate the following for the two projects
i) NPV
ii) IRR
iii) Accumulated profit at 31 December 2014
iv) DPP
Project 1
NPV1=-10000 + 900v +900x1.05v^2 + 900x1.05^2v^3 + 900x1.05^3v^4 + 900x1.05^4v^5 +15000v^5
= -10000 + 900v(1+1.05v + 1.05^2v^2 + 1.05^3v^3 + 1.05^4v^4) + 15000v^5
= -10000 + 900v𝑎̈5¬ @j% + 15000v^5 with j = 1.1/1.05 – 1 = 0.047619
= - 10000 + 900(1.1^-1)(1-1.047619^-5)/0.047619x1.047619 + 15000(1.1^-5) = £3,049.35
IRR1
Set i = 16% (so j becomes 10.476%)
= -10000 + 900(1.16^-1)(1-1.10476^-5)/0.10476x1.10476 + 15000(1.16^-5) = £351.81
Try i =17% (j = 11.4286%)
= -10000 + 900(1.17^-1)(1-1.114286^-5)/0.114286x1.114286 + 15000(1.17^-5) = -£24.28
0.16 + (0-351.81)/(-24.28-351.81)x(0.17-0.16) = 16.9%
A(0,5)1
-10000(1.1^5) + 900(1.1^5)v𝑎̈5¬@j + 15000 = £4,911.01
DPP1
5 years – only turn profit once rights are sold
Project 2
NPV2 = -10000 + 2500v^3 + 18000v^5 = -10000 + 2500(1.1^-3) + 18000(1.1^-5) = £3,054.87
IRR2
Try i = 17%
= - 10000 + 2500(1.17^-3) + 18000(1.17^-5) = -£229.07
Try i = 16%
= -10000 + 2500(1.16^-3) + 18000(1.16^-5) = £171.68
0.16 + (0-171.68)/(-229.07 – 171.68)x(0.17-0.16) = 16.4%
A(0,5)2
-10000(1.1^5) + 2500(1.1^2) + 18000 = £4,919.90
DPP2
5 years – only turn profit once rights are sold
2) A company is considering setting up an operation in a new location it has never operated in.
For the operation to be considered viable it must have an IRR greater than 10%p.a. effective.
The following cashflow projection for the next 10 years has been made. Is the project viable?
Outflows
Between the present time and the opening of the operation in 2 years time the company will
spend £200,000 pa on research, development and marketing of products payable
continuously. The rent on the buildings will be £50,000 pa payable quarterly in advance for
eight years starting in 2 years time. Staff costs are assumed to be £125,000 pa starting in
year 3 and increasing at 5% per annum thereafter. Assume salaries are paid annually in
advance for 8 years.
Inflows
The company expects receive income of £175,000 pa payable continuously for years 3-6,
increasing by £75,000 pa from year 7 until year 10. The company then expects to sell the
operation in 10 years from the present time for £800,000.
Question – if NPV > 0 at i = 10% then viable.
Outgo
200000𝑎̅2¬ + 50000v^2𝑎̈8¬(4) + 125000v^2 𝑎̈8¬ @j% d(4) = 4(1-1.1^-0.25) = 9.4184%, j = 1.1/1.05-1=4.7619%
200000(1-1.1^-2)/ln1.1 + 50000(1.1^-2)(1-1.1^-8)/0.094184 + 125000(1.1^-2)(1-1.047619^-8)
/0.047619x1.047619 = £1,304,516
a) 364,187, b) 234,065 c) 706,264
Income
175000v^2𝑎̅8¬ + 75000v^6(I𝑎̅)4¬ + 800000v^10
175000(1.1^-2)(1-1.1^-8)/ln1. 1 + 75000(1.1^-6)[(1-1.1^-4)/0.1x1.1 – 4(1.1^-4)]/ln1.1 +800000(1.1^-10)
=£1,453,253
NPV = 1453253 – 1304516 = £148,737 so NPV >0 therefore IRR >10%
b) 809,547, b) 335,272 c) 308,435
Question to work through in tutorial
A company is considering setting up an operation in a new location it has never operated in.
For the operation to be considered viable it must have an IRR greater than 10%p.a. effective.
The following cashflow projection for the next 10 years has been made. Is the project viable?
Outflows
Between the present time and the opening of the operation in 2 years time the company will
spend £200,000 pa on research, development and marketing of products payable
continuously. The rent on the buildings will be £50,000 pa payable quarterly in advance for
eight years starting in 2 years time. Staff costs are assumed to be £125,000 pa starting in
year 3 and increasing at 5% per annum thereafter. Assume salaries are paid annually in
advance for 8 years.
Inflows
The company expects receive income of £175,000 pa payable continuously for years 3-6,
increasing by £75,000 pa from year 7 until year 10. The company then expects to sell the
operation in 10 years from the present time for £800,000.
Consider the above question if the criteria was a DPP less than 8 years based on i= 8% pa
Use i = 8% and NPV based on 8 years – if NPV > 0 at t = 8 then DPP <8 yrs
a) 370,736 , b) 207,983 c) 599,971
Outgo
200000𝑎̅2¬ + 50000v^2𝑎̈6¬(4) + 125000v^2 𝑎̈6¬ @j% d(4) = 4(1-1.08^-0.25) = 7.6225%, j = 1.08/1.05-
1=2.8571%
200000(1-1.08^-2)/ln1.08 + 50000(1.08^-2)(1-1.08^-6)/0.076225 + 125000(1.08^-2)(1-1.028571^-6)
/0.028571x1.028571 = £1,178,690
Income
175000v^2𝑎̅6¬ + 75000v^6(I𝑎̅)2¬
175000(1.08^-2)(1-1.08^-6)/ln1.08 + 75000(1.08^-6)[(1-1.08^-2)/0.08x1.08 – 2(1.08^-2)]/ln1.08
=£850,708
NPV = 850708 - 1178690= -£327,982 so NPV <0 therefore DPP >= 8 years
a) 720,978 b) 129,730
