Question

(Ignore income taxes in this problem.) Your Company has a truck that needs a new engine that would cost $35,000. This will extend the useful life of the truck by 5 years. As an alternative, Your Company could buy a brand new truck for $120,000. The new truck would also last 5 years. The annual operating expenses of the old truck are $8,500. The annual operating expenses of the new truck will only be $5,000. The old truck has a salvage value of $12,000 now and $3,500 in 5 years. The new truck is expected to have a $10,000 salvage value in 5 years. Your Company discount rate is 6%. What is the net present value of the decision to buy the new truck instead of repairing the old truck

Answer 1

Answer:

Hence the net cost to the company is 68,160.

NPV to buy a new truck instead of repairing  

NPV = -65390

Explanation:

Step 1:-

P.V. of Old Truck Repaired  

Given  

Discount rate = 6%  

New engine = 35000  

Life = 5 years  

Annual operating expenses = 8500  

Salvage (after 5 years)= 3500

Step 2:-  

Repair  

Net Cost to company  = Cost + Annual operating expenses x P.V. Annuity              

                                               Factor (6%, 5) - Salvage value x P.V. Intrinsic  

                                              Factor (6%, 5)  

 P.V.A.F. (6%, 5)= $\sum_{5}^{1}1 / (1.06)^{n} = 4.21$  

 n = 4.21

 P.V.I.F. (6%, 5) = $1/ (1.06)^{5} =0.75$

 

Net Cost to company:  = 35000 + 8500 x 4.21 - 3500 x 0.75  

= 35000 + 35785 - 2625  

= 68,160

P.V. of New truck purchased  

New Truck  

Cost = 120000  

Discount rate = 6%  

Life = 5 years  

Annual operating expenses = 5000  

Salvage (after 5 years)= 10000  

Net Cost to company:  = Cost + Annual operating expenses x P.V. Annuity

                                           Factor (6%, 5) - Salvage value x P.V. Intrinsic  

                                                                                            Factor (6%, 5)  

= 120000 + 5000 x 4.21 - 10000 x 0.75  

= 120000 + 21050 - 7500  

= 133550

NPV to buy a new truck instead of repairing  

NPV = Net cost of repairing - Net cost of new truck  

= 68160 - 133550  

= -65390