you have the choice of two investments of equal risk. The
required return for both is...
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Finance
you have the choice of two investments of equal risk. Therequired return for both is 8%. The first pays 1500 per month for30 years and starts in 2 years. The second pays 15000 per year inperpetuity, but starts in 3 years. If the cost of both theinvestments is the same, which one would you prefer and why?
Answer & Explanation
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4.4 Ratings (625 Votes)
I would prefer one which has higher present value.
Step-1:Present value of the first option
Present value
=
Annuity
*
Present value of annuity of 1 for 30 years
*
Discount
factor for year 2
=
$Ă‚Â Ă‚Â Ă‚Â Ă‚Â Ă‚Â Ă‚Â 1,500.00
136.2783
*
0.85259
=
$
1,74,284.21
Working:
Present value of annuity of 1 for 30 years
=
(1-(1+i)^-n)/i
Where,
=
(1-(1+0.006667)^-360)/0.006667
i
8%/12
=
0.006667
=
136.2783152
n
30*12
=
360
Discount factor for year 2
=
(1+i)^-n
Where,
=
(1+0.006667)^-24
i
8%/12
=
0.006667
=
0.8525896
n
2*12
=
24
Step-2:Present value of the second option
Present value
=
Present value of cash flow in year 3
*
Discount
factor for year 3
=
(15000/0.08)
*
0.793832
=
187500
*
0.793832
=
$
1,48,843.55
Working:
Discount factor for year 2
=
(1+i)^-n
Where,
=
(1+0.08)^-3
i
8%
=
0.793832241
n
3
So, based
upon present value calculation, first option has higher present
value.So, it is preferable.
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