The revenue generating model for radio and television stations

The primary inventory of radio/television stations is airtime. Radio/television airtimes are used for adverts, paid announcement, sponsored programme, etc. Airtime on radio/television stations is subdivided into three subunits; prime time, fixed time and normal time and the total revenue generated per day by the radio/television station is the sum of revenue from all three subunits of airtime. In this work, we derive the revenue function for each subunit of time and thereafter derive the revenue generating function for the radio/television station. A numerical example is given to demonstrate the use of the model.

Illustrations explain the paper; charts are replotted from the paper's own table values.

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Revenue from adverts: b1 vs b2 vs b3 vs b4 vs b5Close ×

Replotted from Table 1 (page 3) of the original paper. Every bar is the paper's own table value.

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Replotted from source data

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Revenue from adverts: a1 vs a2 vs a3 vs a4 vs a5Close ×

Replotted from Table 2 (page 4) of the original paper. Every bar is the paper's own table value.

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Introduction

The airtime on radio and television stations forms a special type of non-regular fixed lifetime inventory system [1,2,3,4,5] . A non-regular fixed lifetime inventory system is one in which items outdated in one period but become useful in the next period. Simply put, outdated items are not discarded from inventory [6,7] . The usefulness or utility of the items is renewed at the start of the next period. For radio and television stations, a period is a day (1440 minutes) and any minute or multiples of minutes can be used for adverts/paid announcement/sponsored programmes. Any minute not used for adverts/ paid announcement/ sponsored programmes is considered outdate [8,9,10] and whenever there is no airtime/space for adverts/paid announcement in a day, shortage is assumed. Airtime on radio and television stations are classified into prime times, fixed times and normal times. Prime times on radio and television refers to the time of the day when the highest number of people are listening or watching. Prime times can be in the morning or evening, in Nigeria, prime times on radio/television stations are between 6 am -7:30 am in the morning or 8 pm -9 pm in the evening. Advertising rates are highest during prime times [11] because of peak viewing and listening times on television and radio. Besides the regular prime times on radio/television stations, the broadcast of major events such Africa cup of nations, World cup, Olympic games, common wealth games, Europe champions league, etc. creates more prime times for radio/television stations. Commercials can be ran at the start, half way or ending of such major events. Many big, medium and small companies take advantage of the high number of listeners and viewers to advertise their goods and services. Fixed times on radio and television refers to anytime of the day that has been paid for by a company, government agencies or individuals to advertise their goods and services. That time of the day is reserved for the company, agency or individuals. Like other radio/television adverts, fixed time adverts has a minimum duration of one minute and can be extended to any desired number of minutes by the customers. Some fixed time adverts/programmes can run for 2 days, 4 days, 1week, a quarter or even a year and can renewed by the customers if they desire to continue at the end of the period. The price for fixed time adverts is less than that of prime time adverts, since fixed time adverts may run for a long period of time. Fixed time adverts are a major source of revenue for radio and television stations in Nigeria. Normal times on radio/television stations refers to any time that is not prime nor fixed. Adverts rates are lowest during normal times.

There are no permanent normal times on radio, as customers can fix anytime by simply paying for the time, for the desire number of days or quarters. The total revenue of a radio/television station is the sum of revenues from the three subunits of time.

Description of the model

This work is aimed at deriving the total revenue function for a radio/television station. Adverts on radio and television are classified into prime time adverts, fixed time adverts and normal time adverts. The prime time adverts are the most expensive while the normal time adverts are the least expensive. The total revenue for a day is the sum of revenue from all three classes of adverts. Some adverts are only for a period while others can last for more than one period, especially the fixed time adverts. Now if Then the total minutes used for adverts in a day is

Its possible for X to be zero, which means there is no prime adverts for the day. But are hardly zero.

Assumptions and Notations Assumptions

1. The minimum time for a radio/television advert is one minute. 2. The total revenue for a period is the sum of revenues from prime times adverts, fixed times adverts and normal times adverts. 3. There is a fixed operating cost for the radio/television stations. 4. Prime times not used for adverts in a period is considered outdated, but become useful in the next periods. 5. Whenever there is no space/airtime for adverts, shortage is incurred. 6. When a radio/television station suddenly goes off air, there is a periodic penalty for every adverts already paid for until the station comes back on air. 7. The number of days an advert/paid programme can run is not fixed and determined by the customer. 8. The number of minutes for any advert/paid programmes is discrete. 9. There is a fixed number of minutes allocated daily to prime time adverts.

Derivation of total revenue function

The components of the total revenue function for a radio/television station are the revenue functions, the set up cost, the shortage cost, the outdate cost and the penalty cost.

The revenue function

The total revenue per period for radio/television station is the sum of revenues from the prime times, fixed times and normal times.

Prime time revenue

Let the prime time adverts for a day be Its important to note that some fixed time adverts can run for more than a day. If  is the number of days the fixed adverts will run, then the revenue will be Therefore the revenue function by the radio/television per day is given by ( 5) Or ( 6)

Shortage cost

Shortage occur whenever there is no space/airtime for adverts that is every available space for adverts has been booked up. This particularly apply to prime time adverts since the number of minutes allocated to prime time adverts is fixed. So, if the number of minutes X available for prime time adverts is less than the number of minutes Outdate cost outdate occur when the number of minutes allocated to prime time adverts is more than the number of minutes demanded for prime time adverts, that is X X d  .

Outdate cost =

Outdate cost =

Setup cost

There is a fixed set up cost for radio/television stations. Set cost = P

Penalty cost

Whenever a radio/television station is off air as a result of natural disaster or any other reason, a penalty cost is incurred for paid adverts/programmes that cannot be broadcast. Adverts and paid programmes will not be aired. If the radio/television station is off air for n days and the number of prime time adverts, fixed time adverts and normal time adverts affected are z y x q q q , , respectively, the penalty cost will be

are penalty per prime time adverts, fixed time adverts and normal time adverts respectively? The total revenue function for a radio/television station is given by the sum of equations or

Numerical Examples

We give a numerical example to demonstrate the use of the model. A total of ten adverts each, from prime time, fixed time and normal time was documented for a radio station and the total revenue generated for the day was computed with our model. Shortage and outdate were assumed to be zero. A computer programme in Mathematical 8 was designed to carry out the operations. The fixed operating cost was assumed to be 50,000,000.

Conclusion

We have derived the total revenue function for computing the daily revenue for a radio/television station. Airtime on radio/television stations is divided into prime time, fixed time and normal time and the total revenue per day is the sum of revenue from all classes. The model also include costs against radio/television stations such as outdate cost, shortage cost and penalty cost. The stations management aim to minimize the costs and maximize revenue.

Figures and tables from the paper

Class of adverts.	Number of adverts	Duration of advert	Price per minute	Revenue from adverts	advertsR Total revenue from prime time 1
b1	11	1	20,000	220,000	1,300,000
b2	12	2	20,000	480,000
b3	3	3	20,000	180,000
b4	4	4	20,000	320,000
b5	1	5	20,000	100,000
b6	-	-	-	-
b7	-	-	-	-
b8	-	-	-	-
b9	-	-	-	-
b10	-	-	-	-

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Revenue from prime time adverts in a day

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Class of adverts.	Number of adverts	Duration of advert	Price per minute	Revenue from adverts	R Total revenue from fixed time adverts 2
a1	10	1	8,000	320,000	4,672,000
a2	7	2	8,000	448,000
a3	6	3	8,000	1,008,000
a4	2	4	8,000	448,000
a5	8	5	8,000	640,000
a6	4	6	8,000	576,000
a7	3	7	8,000	672,000
a8	2	8	8,000	256,000
a9	1	9	8,000	144,000
a10	1	10	8,000	160,000

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Revenue from fixed time adverts in a day

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Class of adverts	Number of adverts	Duration of advert	Price per minute	Revenue from adverts	R Total revenue from normal time adverts 3
c1	2	1	6,000	12,000	894,000
c2	1	2	6,000	12,000
c3	7	3	6,000	126,000
c4	2	4	6,000	48,000
c5	3	5	6,000	90,000
c6	1	6	6,000	36,000
c7	4	7	6,000	168,000
c8	6	8	6,000	288,000
c9	1	9	6,000	54,000
c10	1	10	6,000	60,000

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Revenue from normal time adverts in a day

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