Topic 8 - Project Appraisal

Question 1

What is project appraisal?

Answer 1

The process of assessing the validity and allowing comparison of investment projects

Question 2

Comment on the nature of cashflows from an investment project

Answer 2

Cashflows of investment projects may consist of a series of inflows and outflows

Question 3

Using information about the cashflows (inflows and outflows) of an investment project what calculations and analysis can we carry out?

Answer 3

Cashflows can be discounted or accumulated to assess

profitability and validity of projects.

Question 4

What are the two methods of determining the profitability and validity of a project?

Answer 4

Accumulated Value

Net Present Value (NPV)

Question 5

What is the Accumulated Value method for project appraisal?

Answer 5

One method is to calculate the accumulated profit at
the end of the project
This method involves calculating the accumulated value of the net cashflows as at the last payment.
A(T) = ∑c,t(1+i)^(T−t)+ ∫0,T ρ(t)(1+i)^(T−t) dt
This figure represents the final amount if all cashflows
were transacted in an account at a rate of i% pa

Question 6

What are the disadvantages of using the Accumulated value method?

Answer 6

There are a couple of problems with this method
-Can only be used when have a definite fixed time horizon for the project
- Problems comparing two projects with different time
horizons

Second problem can be over come by accumulating all profits to the date of the last payment for the longest project
Problems can be avoided by using Net Present Value

Question 7

What is the Net Present Value method for project appraisal?

Answer 7

Net Present Value is the present value at a rate i% pa of net cashflows from an investment project

NPV(i) = ∑c,t(1+i)^(−t) + ∫0,T ρ(t)(1+i)^(−t) dt

i is known as the risk discount rate
A higher NPV indicates a more profitable project

Question 8

Example
Calculate the Net Present Value of the cashflows Ct for the following project using a risk discount rate of 15% pa
C0 =-200, C1 =-100, C2 =+175, C3 =+250

Answer 8

NPV = -200 –100v + 175v^2 + 250v^3
NPV = -200 –100(1.15)^-1 + 150(1.15)^-2 + 250(1.15)^-3
NPV = £9.75

Question 9

What is the Internal Rate of Return?

Answer 9

Internal Rate of Return (IRR) is effective interest that
equates the present value of income and outgo
Rate of i that makes NPV = 0
A higher IRR indicates a more profitable project

Question 10

Example
Calculate the IRR for the following project using a risk discount rate of 15% pa
C0 =-200, C1 =-100, C2 =+175, C3 =+250

Answer 10

For i = 15% NPV = £9.75
i = 16%
NPV(16%) = -200 –100(1.16)^-1 + 175(1.16)^-2 + 250(1.16)^-3 = £4.01
i ≈ 0.15 + (0−9.75)/(4.01−9.75) x (0.16 –0.15) = 16.7%
Perform check to make sure answer is reasonable

Question 11

For a purchase price of £10,000, investor will receive 
£1,000 pa (in arrears) for 20 years
If i = 6% pa calculate:
NPV
IRR

Answer 11

NPV
-10000+1000𝑎20¬ @6% =-10000+1000 x 11.4699 = £1,469.90

IRR
Try 8% -10000 + 1000 x 9.8181 = -£181.90
i ≈ 0.06 + (0−1469.9)/(−181.9−1469.9) x (0.08 –0.06) = 7.8% (check)

Question 12

Comparing two investments

Investment 1
For a purchase price of £20,000, investor will receive £2,000 pa (in arrears) for 15 years
Investment 2
For a purchase price of £22,000, investor will receive £1,200 pa (in arrears) for 18 years, plus a return of the capital
Investor can borrow or lend at 4%, should the investor invest in any of the investments, if so which is most profitable?

Answer 12

Investment 1
Calculate NPV = -20000 + 2000 𝑎15¬ @4%
NPV = -20000 + 2000 x 11.1184 = £2,236.80
Calculate IRR
@ 5% -20000 + 10.3797x2000 = £759.4***
@ 6% -20000 + 9.7122x2000 = -£575.6
i ≈ 0.05 + (0−759.4)/(−575.6−759.4) x (0.06 –0.05) = 5.57% pa OR
Calculate IRR
Solve 20000/2000 = 𝑎15¬ = 10
𝑎15¬ @5% = 10.3797 and 𝑎15¬ @6% = 9.7122
i ≈0.05 + (10−10.3797)/(9.7122−10.3797) x (0.06 –0.05) = 5.57% pa

Investment 2
Calculate NPV = -22000 + 1200 𝑎18¬ + 22000v18
NPV = -22000 + 1200x12.6593 + 22000x1.04^-18 = £4,050.98
Calculate IRR
Solve -22000 + 1200 𝑎18¬ + 22000(1+i)^-18 = 0
@ i =5% NPV = £1,168.97 @ 6% NPV = -£1299.31
i ≈0.05 + (0−1168.97)/(−1299.31−1168.97) x (0.06 –0.05) = 5.47% (check)

Investment 1
NPV = £2,236.80
IRR = 5.57%
Investment 2
NPV £4,050.98
IRR = 5.47%
Since rate they can borrow and lend is 4% pa, compare NPV, so investment 2 is most profitable
However if rate borrow and lend was 5.5% pa then investment 1 would be most profitable (as 2 would produce a loss)

Question 13

What is the reality for investors regarding borrowing and lending rates?

Answer 13

So far we have assumed that investor may borrow and
lend money at same rate
In reality may have to borrow at a higher rate (j1) than
they lend money at (j2)
So IRR & NPV may be of limited use in this case

Question 14

When is the DPP useful?

Answer 14

Discounted Payback Period (DPP) is useful for project financed by outside money

Question 15

What is the DPP?

Answer 15

DPP is number of years before project is profitable

Question 16

Give the theory and formula behind the DPP

Answer 16

DPP is number of years before project is profitable
So it is the smallest value of t such that A(t)≥ 0, where
A(t) = ∑c,s(1+j1)^(t−s) + ∫0,t ρ(s)(1+j1)^(t−s) ds for s≤t

Question 17

If project viable such that DPP occurs, A(t)≥0, the accumulated profit at time T (at j2) is

Answer 17

j1 is rate investor borrows at
j2 is rate investor lends at
j1>j2
If project ends at t=T and A(T) < 0, then no DPP
If project viable, accumulated profit at T (at j2) is
P = A(t1)(1+j2)^(T-t) + ∑c,t(1+j2)^(T−t) + ∫t1,T ρ(t)(1+j2)^(T−t) dt for t>t1

Question 18

Discounted Payback Period
Example
Investor borrows £100,000 at effective rate of 10% pa to finance a project that will pay £15,000 pa (in arrears) for next 14 years. Find DPP?
A(t) = -100000(1+i)^t + 15000 𝑠t¬

Answer 18

A(t) = -100000(1+i)^t + 15000 𝑠t
A(t) = -100000(1+i)^t + 15000(1+i)^t x 𝑎t¬
Profit when -100000(1+i)^t + 15000(1+i)^t x 𝑎t¬ ≥0
Rearrange and divide by (1+i)^t
t =11 = -100000 +15000x6.4951 = -£2,574
t=12 = -100000 + 15000x6.8137 = £2,206
DPP is 12 years

Alternatively, Rearrange and divide by 15000(1+i)^t
𝑎t¬ ≥100000/15000 = 6.667
𝑎11¬ = 6.4951 𝑎12¬ = 6.8137 @ 10%
DPP is 12 years

Question 19

Q) For a purchase price of £10,000, investor will receive £1,000 pa (in arrears) for 20 years
Investor can borrow or lend at 6% calculate the DPP

Answer 19

DPP
A(t) = -10000(1+i)^t + 1000(1+i)^t x 𝑎t¬
Want 𝑎t¬ ≥10000/1000 = 10
𝑎15¬ = 9.7122 𝑎16¬ = 10.1059, so DPP is 16 years

Question 20

In addition to the methods discussed an investor would also consider what factors?

Answer 20

Cashflows
Resources
Borrowing requirements
Risk
Investment conditions
Cost vs benefit
Indirect benefits

Question 21

Other factors to consider

Why are cashflows a factor to consider before investment in a project?

Answer 21

• Are cashflows consistent with business’ needs
• What will the accumulated profit be
• Over what period will the profits be produced
• Is it worthwhile if potential profit very small

Question 22

Other factors to consider

Why are resources a factor to consider before investment in a project?

Answer 22

• Are the required resources available

* Do they have the necessary staff, expertise and equipment

Question 23

Other factors to consider

Why are borrowing requirements a factor to consider before investment in a project?

Answer 23

• Can they raise the necessary cash at the required time
• What rate of interest will they have to pay
• Are there any restrictions imposed on borrowing

Question 24

Other factors to consider

Why is risk a factor to consider before investment in a project?

Answer 24

• Financial risks involved
• How certain are they about the risk discount rate to use
• Is there the possibility for unlimited loss
• Can you rely on suppliers to fulfil their contracts

Question 25

Other factors to consider

Why are investment conditions a factor to consider before investment in a project?

Answer 25

• What is the economic climate

* Are interest rates likely to rise or fall

Question 26

Other factors to consider

Why is cost vs benefit a factor to consider before investment in a project?

Answer 26

• Is project worth doing

* Do the costs outweigh the benefits

Question 27

Other factors to consider

Why are indirect benefits a factor to consider before investment in a project?

Answer 27

• Will project bring any additional benefits

* Will equipment and skills attained be of future benefit