Question

Little Jack Horner is tired of sitting in the corner and wants to attend college. In fact, he intends to go to Harvard when he is old enough and he wants to major in nursery rhyme writing. He will stay in school for 4 years after which he will have a BA degree. His father, Humpty Dumpty, is sympathetic with Jack’s aspirations, but he believes Jack must take care of him first. Therefore, Humpty will finance Jack’s education with a bequest at his death and, until that time, Jack is to look after his father. Harvard will cost $50,000 per year for the four years (payable at the beginning of each year) and Humpty specifies in his Will, that, at his death, the necessary funds will be deposited in an account paying 10% annual interest. Jack will begin college immediately after Humpty’s death

Humpty will retire 20 years before his death and during his retirement he wants to have $100,000 per year (beginning-of-year). The funds necessary for Jack’s education as well as Humpty’s retirement pay will come from an amount he will have accumulated during his remaining working years. Upon his retirement, Humpty plans to invest all of his funds into an account which will earn 10% annual interest (this rate will be earned during Humpty’s retirement years and during Jack’s college years).

Currently Humpty does not have any money saved; however, he plans to retire 15 yearsfrom now. Humpty wants to accumulate enough funds over his remaining 15 working years to enable him to fulfill his plans as described above. Humpty plans to accumulate the necessary funds in two ways:

1. He just purchased 1,000 shares of SkyRocket company common stock for $20 per share. He believes that the price will increase at a 20% annual rate and he will sell the stock when he retires. He does not expect the stock to pay a dividend over the next 15 years.

2. He will put aside a fixed amount at the end of each year beginning this year (during his working years) in an IRA which he will withdraw at the end of his working period (ignore taxes). The IRA will pay 10% annual interest.

What annual payment must Humpty make into the IRA account in order to carry out his plans? Please provide a timeline, a description of all of your math, and calculator inputs.

Part B A firm has estimated its cost of capital as 5% and is considering a project with an initial investment of -$265,000. The subsequent cash flows are $65,000; $77,000; $83,000; $91,000; and $96,000. In the final year (year #6), the firm must pay $50,000 to clean up the site. Calculate the project’s MIRR using the three methods discussed in class (Discounting method, Reinvestment approach, Combination approach). Please provide timelines, a description of all of your math, and calculator inputs.

Answer 1

Here are the timelines from now to the end of college

Assumption

now there is one thing which is not clear the question, on one hand, it says that Humpty doesn't have any money with him but in the other hands he bought shares of 20000 dollars which means he might have borrowed this money from somewhere but since the details of borrowing like borrowing rate and period repayment structure are not given in the question we have to assume that he had this was his own money.

we have assumed the annual IRA deposits as X now let'sp find the value of X

PV of all outflows now= PV of All inflows now

PV of college fees at humpty's death=50000((1-1.1^(-4))/0.1)*1.1=174342.6

PV of college fees now=174342.6/(1.1)^ (15+20)=6203.82

PV of humpty's retirement pay at humpty's retirement=100000((1-1.1^(-20))/0.1)*1.1=936492

PV of humpty's retirement pay now 936492/1.1^15=224188.74

PV of outflows now=224188.74+6203.82=230392.57

PV of X now= X*(1-1.1^(-15))/0.1=7.606079*X

PV of Share receipt now=(20000*102^15)/1.1^15=73766.37

now we have

73766.37+7.606079*X=230392.57

solving for X we get X( IRA deposit)=20592.24

Part B:

timeline

MIRR using Discounted method ( recommended in this case since the CASHFLOWS ARE OF NON-CONVENTIONAL PATTERN

STEP 1 pv of all cash outflow at the company's cost of capital Kc which is 5%

265000+50000/1.05^6=302310.76

STEP 2 fv of cash inflows at the company's reinvestment rate 10%assumed

65000*1.1^5+77000*1.1^4+83000*1.1^3+91000*1.1^2+96000*1.1^1=543601

STEP 3 Equate step 1 and 2 as follows

543601.85/(1+m)^6 = 302310.76

m= MIRR = 10.27%

reinvestment method

FV of All future CF at reinvestment rate

which is =543601-50000=493601

equate it with initial cash inflows i. e. 265000

265000(1+m)^6=493601

m=MIRR=10.92%