Question

Class Handout Checked Understanding the IRR There are two things investors worry about: risk and return This helps us understand something about "return." Story #1 Suppose you put money in a bank, and made withdrawals as follows: Rate Month Beg Bal Interest E Withdrav Deposit End Balance 158 10 118 Please find the "IRR" that would turn your deposit into your withdrawals. Fill in the table: hint: the last ending balance should be zero. Story #2 This is the same story, except that the order of withdrawal's is different. Rate Month Beg Bal - Interest Evithdrawe Deposit End Balance 158 118 73 40 Again, please find the IRR and fill in the table. Thought provoking question: are you getting a feel for the IRR Thought provoking question: Why is the IRR higher for story #22 Based on the tables, what is the difference in ending balances for month 3? A Between 10 and 84 B Between 84 and 89 C Between 89 and 94 D Between 94 and 99

Answer 1

Solution:

For Story 1, the cash flows are shown as:

t=0	t=1	t=2	t=3	t=4
-158	10	40	73	118

Using IRR function, we can compute the IRR as 14.159%. [In excel, IRR can be calculated as =IRR(range of values)]

The table can be computed as:

Month	Beg. Balance	Interest Withdrawl	Deposit	End Balance
0			158	158.00
1	158.00	10	0	=158*(1+14.159%)-10=170.37
2	170.37	40	0	=170.37*(1+14.159%)-40=154.49
3	154.49	73	0	=154.49*(1+14.159%)-73=103.37
4	103.37	118	0	=103.37*(1+14.159%)-118=0.00

For Story 2, the cash flows are as follows:

t=0	t=1	t=2	t=3	t=4
-158	118	73	40	10

Using IRR function, we can compute the IRR as 28.79%. [In excel, IRR can be calculated as =IRR(range of values)]

The table can be computed as:

Month	Beg. Balance	Interest Withdrawl	Deposit	End Balance
0			158	158.00
1	158.00	118	0	=158*(1+28.79%)-118=85.48
2	85.48	73	0	=85.48*(1+28.79%)-73=37.09
3	37.09	40	0	=37.09*(1+28.79%)-40=7.76
4	7.76	10	0	=7.76*(1+28.79%)-10=0.00

IRR is higher in the second case because of the declining withdrawals, i.e., a higher amount of withdrawals in the initial years and of the lower amount in later years. IRR is also considered as a reinvestment rate, hence, in the second case, the remained amount after each withdrawal has to be reinvested at a higher rate to cater to the subsequent period's withdrawals.

The difference between the ending balance of period 3 in both case is calculated as = 103.37-7.76 = 95.60

Hence, Option D is the answer