Entering Numerical Sequences When Sequential Values Are an Initial Value Plus a Constant

FNR 407 Lab. Exercise #1 Handout to accompany Excel spreadsheet Due at end of class

Summation Notation

Capital letters are columns in the spreadsheet j is the index across columns or rows

Numbers are rows in the spreadsheet

10. Entering numerical sequences when sequential values are an initial value plus a constant incremental value, e.g. 1, 2, 3; or 2, 4, 6

1. Enter the starting value of the sequence 2. In the next cell enter a formula giving the next value as the starting value plus the amount of the increment.

K L42 = ∑ j 42 j = B where, “42” is row 42 in the spreadsheet, and B through K are columns in the spreadsheet. Thus, this notation means,

B42 + C42 + . . . + K42

11. Entering numerical sequences when sequential values are an initial value plus a constant incremental value, e.g. 1, 2, 3; or 2, 4, 6 1. Enter the starting value of the sequence 2. In the next cell enter a formula giving the next value as the starting value plus the incremental value.

K D46 = ∑ j 46 j = B where, 46 is row 46 in the spreadsheet, and B through K are columns in the spreadsheet

59 B60 = ∑ Bj j = 50 where, B is the column in the spreadsheet, and 50 through 59 are rows in the spreadsheet

74 D76 = ∑ (Bj * Cj)^2 j = 65

90 D91 = ∑ (Bj * Cj)/(1.03^2) j = 81

103 E104 = ∑ (Bj - Cj)/((1+$D$96)^Aj) j = 98 EXCEL Financial Functions

Future Value Function

FV(rate, number of periods, payment, The value of an investment at the end of present value, type) the term (0 if omitted) Argument Description Interest rate, enter as “x%” Annual compound rate of interest Number of periods Term of the investment Payment (negative values indicate Annual payments when individual amounts payments into an investment, positive are the same values indicate payments out of an investment) Present value Starting value that’s in addition to the annual payments (See FV Example 2) Type When payment is to be made (0 if omitted); 0 = at end of period; 1 = at beginning of period (In class I’ll refer to this as year 0)

FV Example 1. You plan to contribute $4,000 in an Individual Retirement Account (IRA) at the beginning of each year. You expect the average rate of return to be 6% per annum. You are now 30 years of age. How much should be in the account when you are 65 years of age?

FV(6%, 35, -4000,,1) =$472,483.47

FV Example 2. Building on FV Example 1, assume you started your IRA 3 years ago. The amount in the IRA is $7,500 to start with.

FV(6%,35,-4000,-7500,1) = $530,129.12

Present Value Function

PV(rate, number of periods, payment, Value of an investment today, i.e. in year future value, type) zero (beginning of year 1) Argument Description Interest rate, enter as “x%” Annual compound rate of interest Number of periods Term of the investment Payment Annual payments when individual amounts are the same Future value Ending value that’s in addition to the annual payments (See PV Example 2) Type When payment is to be made (0 if omitted); 0 = at end of period; 1 = at beginning of period (In class I’ll refer to this as year 0) PV Example 1. You have the opportunity to invest $4,000 in a start-up company. The entrepreneur guarantees you $1,000 per year for the next 5 years in return for taking a risk on his enterprise. If you don’t make this investment you would buy a 5-year certificate of deposit (CD) with a 4.5% rate of return. Which is your best option, ignoring the difference in the risk?

PV(4.5%,5,1000,,0) = -$4,389.98 (function could be entered as PV(4.5%, 5,1000)

Since the PV of the payments is greater than the amount you would be investing the investment in the start-up would provide a greater rate of return than the CD, i.e. the start-up is the best option.

PV Example 2. What if the entrepreneur offers you $5,000 at the end of 5 years, instead of $1,000 per year for 5 years?

PV(4.5%,5,,5000,0) = -$4,012.26 (function could be entered as PV(4.5%,5,,5000)

The PV is still greater than the $4,000 investment so the investment is acceptable, but not as good as the annual payment option. TAKE AWAY – Getting your money back sooner, rather than later, is always better financially.

Net Present Value Function

NPV(rate, value1, value2, . . .,value n) Present value of a series of periodic inflows and outflows from an investment Argument Description Interest rate, enter as “x%” Annual compound rate of interest value1, value2, . . ., value n Series of annual net amounts NOTE: all payments are assumed to occur at the end of each year.

NPV Example 1. You have the opportunity to buy for $1,500,000 a farm with all the acreage suitable for wildlife habitat. Over the first year you’d need to make $100,000 of improvements. Thereafter you would have annual expenses of $25,000 and annual rental income of $75,000. You expect to retire in 10 years at which time you would sell the farm for an estimated $3,000,000. Your alternative rate of return (hurdle rate) is 6%. Is this a good investment?

NPV(6%,-100000,50000,50000,50000,50000,50000,50000,50000,50000,50000,3050000)-1500000 = $401,679.25

Since the NPV is greater than zero this investment would earn you more than the 6% alternative rate of return you require. It’s a good investment. Payment Function

PMT(rate, number of periods, present annual or monthly payment needed to pay value, future value, type) off an amount borrowed in year 0 Argument Description Interest rate, enter as “x%” for annual Annual compound rate of interest, or payments, “x%/12” for monthly payments equivalent monthly rate Number of periods, for monthly payments Term of the loan multiply the number of years by 12 Present value Amount borrowed in year 0 Future value Lump-sum payment at end of period Type When payment is to be made (0 if omitted); 0 = at end of period; 1 = at beginning of period (In class I’ll refer to this as year 0)

PMT Example 1. You want to buy a new log truck for $120,000 with a $10,000 down payment and the balance paid off over 5 years with payments made at the end of the year. The bank will charge 5.5% interest.

PMT(5.5%,5,110000,,0) = -$25,759.41

PMT Example 2. What would the monthly payments be for the loan in example 1.

PMT((5.5%/12),(5*12),110000,,0) = -$2,101.13

PMT Example 3. How much would you have to pay each month into a savings account earning 5.5% interest if you wanted to have $120,000 to buy a new logging truck in 5 years.

PMT(5.5%,5,,120000,0) = $1,742.14

Rate Function

RATE(number of periods, payment, Given the amount of payments made, it present value, future value, type, guess) estimates interest rate needed to pay off a loan, or to have a set amount at the end of the period. Argument Description Number of periods Number of years or months Payment Amount of annual or monthly payment made Present value Amount to be paid off Future value Amount needed in the account at end of period Type When payment is to be made (0 if omitted); 0 = at end of period; 1 = at beginning of period (In class I’ll refer to this as year 0) Guess Your estimate of the interest rate. This becomes the starting point for the iterative process used.

RATE Example 1. You are planning on buying a tract of forestland as an investment. There is a tract available for $550,000. You can afford to $60,000 a year. If you want to pay off the loan in 15 years what interest rate would you need to negotiate to make this work?

RATE(15,-60000,550000) = 6.9000%

RATE Example 2. If instead or borrowing money to make a forestland investment you want to save the money first. You think you’ll need $500,000 in 10 years to buy a tract and you can afford to save $40,000 a year. What rate of interest would the account have to earn to achieve your goal?

RATE(10,-40000,,500000) = 4.8669%

Internal Rate of Return Function

IRR(values, guess) For a given array of cash flow values the rate of interest that makes the NPV for this array equal to 0 is estimated Argument Description Values An array of net annual values. Must be at least 1 each of positive and negative values. Guess Starting interest rate for the iterative process NOTE: This function doesn’t account for year 0 net revenue

IRR Example 1. You’re considering the possibility of starting a business. The array of revenues and expenses by year is:

Row in A B C D Excel 1 Year Revenue Expense Net Revenue (revenue - expenditures 2 1 $0 $140,000 -$140,000 3 2 $10,000 $55,000 -$45,000 4 3 $200,000 $10,000 $190,000 5 4 $150,000 $15,000 $135,000 6 5 $90,000 $20,000 $70,000 IRR(D1:D6,10%) = 37.2558%

This would be an exceptionally good investment.