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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 Solved by verified expert
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
= $       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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