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Hi John, please give me an insight into how to solve the problem below:
A company has agreed to lease a machine for a period of 8 years with equal annual payments at the start of each year.
The NPV of the agreement at the rate of 10% is £52,000
What is the annual lease payment.What I did was to divide the NPV by 8years annuity @10% but that was obviously wrong, please help!
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I think it’s actually right.
if we take annual payments as Y.
10% annuity of 8 years x Y = 52000
5.335 x Y = 52000
Therefore Y = 52,000 / 5.335
Y = 9747 (rounded)
meaning 8 annual payments of 9747 will be made, totalling £77976
remember, the annual amount should be higher because it will be discounted in future years.- Topics: 0
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I’m looking at my BPP book with a very similar question:
Brown co has decided to invest in a new machine which has a 10 year life and no residual value. Themachine can either be purchased now for $50,000, orit can be leased for 10 years with lease rental payments of $8,000 per annum payable at the end of each year.
The cost of capital is 9% and taxation should be ignoredSolution
PV = Annuity factor at 9% for 10 years x $8.000
= 6.418 x $8,000 = $51,344All i’ve done above is re-arrange the formula so i don’t understand?
Aleksandrs: Your answer is wrong – there is one big difference between the question and the one in the BPP book – look at when the first payment is made!!!
Dapidod: Suppose the lease payment is X per year.
The first payment is immediate (it is paid at the start of the year), so the PV is X.
There are then 7 payments. The PV of these is 4.868X (4.868 is the 7 year annuity factor).
So the total PV is X + 4.868X = 5.868XThis must be equal to 52,000
So X = 52,000 / 5.868 = $8862
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