Example $9$: Austin, a pet food manufacturer, developed a patented blend of nutritional food for dogs and has licensed its international sales to Pheonix inc for $25$ years. Under this arrangement, Pheonix inc will p$.$ a constant payment of $$50,000$ per year for the next $25$ years, beginning one year from now and a single payment of $$1$ million after $25$ years. If a discount rate of $6$ percent is applied, how much is this license dea worth now? Apply the correct formula in cell C$168.$ The output will be negative, but, you have to ignore the negative sign because according to the question, we just need to find the present worth of this deal and this $PV$ will not be actually paid by Austin to Pheonix inc Thus, we want a positive value, and so we will use and not $=$PVO.

PV

EPVO

$!$

Status: Enter function

Example $10$: Austin is planning to have another licensing deal with a different firm $-$ Milo LLC$.$ In this proposed arrangement, Milo LLC is planning to pay $$60,000$ each year and a lump sum payment of $$500,000$ a the end of the last year of this arrangement. The management at Austin believes that the value of the license and the interest rate in this arrangement with Milo LLC should be the same as those in the arrangemer with Pheonix inc $($example $9).$ The management approached you to determine the duration of this proposed arrangement with Milo LLC such that there is no loss or gain in the value of the license to use this patented formulation of nutritional dog food. Apply the NPERO function in cell C$170.$

You need to use the nper $0$ function in this case. The nper $0$ function has the following syntax $=$ NPER$($rate$,$pmt$,$pv$,[$fv$],[$type$]).$ Like PVO and FVO functions, make sure that the rate of interest has the same period a the compounding period. The output of this function will tell you how many number of such periods should be there such that the present value $($pv$)$ now is equal to the payments in future $($pmt$)$ and the lump sum value $($future value$)$ at the given interest rate, according to the concepts of Time Value of Money.

Do not forget to use pv with a negative sign, and pmt and fy with positlve signs, because, as mentioned before, at least one cash flow has to be of the opposite sign. Since, PMT and FV are cash inflows for Austin, consider them to be positive. Thus, we have to assume that PV is negative, even though this amount is never exchanged. If we do not have at least one out of PV$,$ PMT or FV of the opposite sign, the NPERO function will throw an error or give a negative value which will be a valid mathematical solution but is not intuitive as the number of periods cannot be negative in Finance. You cannot time travel in the past to exchange a future cash flow and call that amount as the Puture Valuel $($Or can you?$)$

NPER

Show All Functions

PV

Rate $=$ number

Nper $=$ number

Pmt $=$ number

$Fv=$ number

Type $=$ number

Result: $(...\}$

$f_{x}PV$