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A company has decided to lease a machine. Six annual payments of $8,000 will be made with the first
payment on receipt of the machine. Below is an extract from an annuity table:
Year Annuity factor
10%
1 0.909
2 1.736
3 2.487
4 3.170
5 3.791
6 4.355
What is the present value of the lease payments at an interest rate of 10%?
A $30,328
B $34,840
C $38,328
D $48,000my question is why don’t we multiply 8000 by 4.355 as it says 6 years?
We would use the 6 year annuity factor if the flows were at times 1 to 6 (i.e. the first payment being in 1 years time), as I explain in my free lectures on this.
However that is not the case in that the first payment is immediately, i.e. at time 0. After the payments are at time 1 to 5.
Therefore the PV is 8,000 + (8,000 x the 5 year annuity factor)
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