Question

you have the choice of two investments of equal risk. The required return for both is 8%. The first pays 1500 per month for 30 years and starts in 2 years. The second pays 15000 per year in perpetuity, but starts in 3 years. If the cost of both the investments is the same, which one would you prefer and why?

Answer 1

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.