Question

As a special advisor to Special Road Infrastructure Development, you have been approached by the Minister to evaluate the financial viability of three alternative road improvement projects. Project data are captured in Table 3.1:

Table 3.1: Municipal Road improvement project

	Alternative A	Alternative B	Alternative C
Initial cost R	7 500 000	8 500 000	9 500 000
Annual maintenance costs, R	200 000 for the first 18 years then 250 000 over the remaining 12 years	R190 000 for the first 20 years and R220 000 over the remaining years 15 years	R170 000 for the first 30 years and R190 000 over the remaining years 10 years
Annual Energy Costs, R	200 000	180 000	160 000
Annual Revenue, R	350 000	450 000	600 000
Salvage Value, R	950 000	1200 000	1 400 000
Economic Life, years	30	35	40
Discount rate p.a.	12.5%	12.5%	12.5%

       

Using Net Present Value analysis, determine which of the project alternatives is worth implementation.

(Hint: F = P ( 1+i )ⁿ ;    P = A [ (1+i)ⁿ – 1] / [ i * (1+i)ⁿ])  

Answer 1

F = P ( 1+i )ⁿ ;    PVAF = A [ (1+i)ⁿ – 1] / [ i * (1+i)ⁿ];  PVIF = 1 / (1 + i)ⁿ

Net Present Valye = Present value of cash inflow - Present value of cash outflows

PVAF(18/0.125)=1(1−(1+0.125)^−18/ 0.125)

=1(1−0.120020269037840.125)

=1(7.0398378476973)

=7.0398378476973

PVAF(12/0.125)=1(1−(1+0.125)^−12/ 0.125)

=1(1−0.24331547469230.125)

=1(6.0534762024616)

=6.0534762024616

PVAF(30/0.125)=1(1−(1+0.125)^−30/ 0.125)

=1(1−0.0292027887336390.125)

=1(7.7663776901309)

=7.7663776901309

PVIF(18/0.125) = 1/(1+0.125)^18 = 0.1200

PVIF(30/0.125) = 1/(1+0.125)^30 = 0.0292

Alternative A:

Cash outflow = P.V. of initial cost + P.V. of annual maintenance cost + P.V. annual energy cost - P.V. of salvage value

= 7,500,000 + 200,000*PVAF(12.5%, 18) + 250,000*PVAF(12.5%,12)*PVIF(12.5%,18)
+ 200,000*PVAF(12.5%,30) - 950,000*PVIF(12.5%,30)

= 7,500,000 + 200,000*7.0398 + 250,000*6.0535*0.1200 +
200,000*7.7664 - 950,000*0.0292

= 7,500,000 + 1,407,960 + 181,605 +1,553,280 - 27,740

= 10,615,105

Cash inflow = P.V. of annual revenue

= 350,000*PVAF(12.5%,30)

= 350,000*7.7664

= 2,718,240

NPV = 2,718,240 - 10,615,105 = -7,896,865

Alternative B:

Cash outflow = P.V. of initial cost + P.V. of annual maintenance cost + P.V. annual energy cost - P.V. of salvage value

= 8,500,000 + 190,000*PVAF(12.5%, 20) + 220,000*PVAF(12.5%,15)*PVIF(12.5%,20)
+ 180,000*PVAF(12.5%,35) - 1,200,000*PVIF(12.5%,35)

= 8,500,000 + 190,000*7.2413 + 220,000*6.6328*0.0948
+ 180,000*7.8703 - 1,200,000*0.0162

= 8,500,000 + 1,375,847 + 138,334 + 1,416,654 - 20,160

= 11,410,675

Cash inflow = P.V. of annual revenue

= 450,000*PVAF(12.5%,35)

= 450,000*7.8703

= 3,541,635

NPV = 3,541,635 - 11,410,675 = -7,869,040

Alternative C:

Cash outflow = P.V. of initial cost + P.V. of annual maintenance cost + P.V. annual energy cost - P.V. of salvage value

= 9,500,000 + 170,000*PVAF(12.5%, 30) + 190,000*PVAF(12.5%,10)*PVIF(12.5%,30)
+ 180,000*PVAF(12.5%,40) - 1,400,000*PVIF(12.5%,40)

=  9,500,000 + 170,000*7.7664+ 190,000*5.5364*0.0292
+ 180,000*7.9280- 1,400,000*0.0090

= 9,500,000 + 1,320,288 + 30,716 + 1,403,640 - 12,600

= 12,242,044

Cash inflow = P.V. of annual revenue

= 600,000*PVAF(12.5%,40)

= 600,000*7.9280

= 4,756,800

NPV = 4,756,800 - 12,242,044 = -7,485,244

Since the NPV is maxium for Alternative C among all three alternative available, the company should implement alternative C.

Although, none of the NPV is positive, we are considering the highest among the three.