Question

The subscription to a magazine is currently priced at $5 per year, with the subscription price set to increase by 1% per year into perpetuity. The publisher is also currently offering a perpetual subscription to this magazine for a fixed price of $90. The Cost of Capital is 6%. Which of these offers is cheaper to the subscriber, i.e. is best for the subscriber, based only on the information provided herein?

	a.	The perpetual subscription
	b.	The annual subscription
	c.	They both have equal value
	d.	They both have no value

Answer 1

- Current Annual Subcription amount = $5

Subscription price set to increase by 1% per year into perpetuity

If cost of Capital is 6%

calculating the Present Value of annual subscription:-

where, = Annual Subscription = $5

g = growth rate = 1% per year

r = cost of capital = 6%

Present value = $101

So, Today cost or Present Value of annual subscription is $101

- Fixed price of perpetual subscription to this magazine =$90

As the Fixed Price(or Present Value) of perpetual subscription is less than that of Annual Subscription, Perpetual Subscription is cheaper.

Thus, Option A

If you need any clarification, you can ask in comments.    

If you like my answer, then please up-vote as it will be motivating