# A Theoretical Framework for Estimating the Rate of Return to a Pharmacy Education Anywhere

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Step 1. Model Output: Choice of Nominal or Real Rate of Return

#### 2.2. Step 2. Model Assumptions: Personal Characteristics

#### 2.3. Step 3. Model Inputs: Costs and Benefits of the Pharmacy Education Investment

#### 2.3.1. Costs

#### 2.3.2. Benefits

## 3. Results

_{1}represents the cost of tuition, E

_{1}represents the cost of the other school-related expenses, F

_{1}represents the interest paid on the amount borrowed to pay for tuition and/or other school-related expenses, O

_{1}represents the opportunity cost of not working, and C

_{1}is the sum of these four cost categories. There is no B

_{1}because the individual is not working as a pharmacist yet. In the following year, Year 2, T

_{2}, E

_{2}, and F

_{2}may or may not be the same as T

_{1}, E

_{1}, and F

_{1}, respectively, depending on the assumptions in the model; O

_{2}, however, would be equal to O

_{1}plus the percentage gain in productivity (PG

_{2}) plus, if applicable, the anticipated annual inflation rate.

_{h}

_{+ 1}consistent with prorated work may be appropriate. Regardless of the existence of a gap, a realistic initial level of earnings, commensurate with the considerations discussed in Step 4, should be entered. This level also should take into account possible bonuses and the likelihood of additional pay because of overtime work. For the following year a percentage increment in productivity (PI

_{h}

_{+ 2}) should be added to the annualized amount of earnings of Year h + 1. This percentage increase has been denoted differently from the percentage added to the opportunity cost to accommodate the argument that a pharmacist’s percentage gain in productivity may be different from the gain in productivity of a non-pharmacist. Beyond Year k the opportunity cost is the only cost remaining in the model.

_{t}is the amount of professional income earned by the pharmacist in Year t; C

_{t}is the total amount of costs incurred by the pharmacist in Year t (C

_{t}= T

_{t}+ E

_{t}+ F

_{t}+ O

_{t}); and r is the rate of return; and where t = 1, …, n; and n is the number of years in the pharmacy education investment span, from entering pharmacy school to retirement.

_{t}, C

_{t}, and n is illustrated in Table 1. Specific applications to benefits, costs, and worklife span in the USA are presented by Carvajal and Popovici [6].

## 4. Discussion

## 5. Limitations

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## IRB Approval

## References

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**Table 1.**Hypothetical chart summarizing estimated annual costs and benefits related to a pharmacy education investment.

Year (t) | Costs * | Benefits (B _{t}) | Benefits Minus Costs (B _{t} − C_{t}) | ||||
---|---|---|---|---|---|---|---|

School-Related | Financing (F _{t}) | Opportunity (O _{t}) | Total (C _{t}) | ||||

Tuition (T _{t}) | Expenses (E _{t}) | ||||||

1 | T_{1} | E_{1} | F_{1} | O_{1} | C_{1} | - | −C_{1} |

2 | T_{2} | E_{2} | F_{2} | O_{1} + PG_{2} | C_{2} | - | −C_{2} |

… | |||||||

h | T_{h} | E_{h} | F_{h} | O_{h} _{− 1} + PG_{h} | C_{h} | - | −C_{h} |

h + 1 | - | - | F_{h} _{+ 1} | O_{h} + PG_{h} _{+ 1} | C_{h} _{+ 1} | B_{h} _{+ 1} | B_{h} _{+ 1} − C_{h} _{+ 1} |

h + 2 | - | - | F_{h} _{+ 2} | O_{h} _{+ 1} + PG_{h} _{+ 2} | C_{h} _{+ 2} | B_{h} _{+ 1} + PI_{h} _{+ 2} | B_{h} _{+ 2} − C_{h} _{+ 2} |

… | |||||||

k | - | - | F_{k} | O_{k} _{− 1} + PG_{k} | C_{k} | B_{k} _{− 1} + PI_{k} | B_{k} − C_{k} |

k + 1 | - | - | - | O_{k} + PG_{k +} _{1} | C_{k +} _{1} | B_{k} + PI_{k} _{+ 1} | B_{k} _{+ 1} − C_{k} _{+ 1} |

… | |||||||

n | - | - | - | O_{n} _{− 1} + PG_{n} | C_{n} | B_{n} _{− 1} + PI_{n} | B_{n} − C_{n} |

_{t}= T

_{t}+ E

_{t}+ F

_{t}+ O

_{t}.

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**MDPI and ACS Style**

Carvajal, M.J.; Popovici, I.
A Theoretical Framework for Estimating the Rate of Return to a Pharmacy Education Anywhere. *Pharmacy* **2020**, *8*, 162.
https://doi.org/10.3390/pharmacy8030162

**AMA Style**

Carvajal MJ, Popovici I.
A Theoretical Framework for Estimating the Rate of Return to a Pharmacy Education Anywhere. *Pharmacy*. 2020; 8(3):162.
https://doi.org/10.3390/pharmacy8030162

**Chicago/Turabian Style**

Carvajal, Manuel J., and Ioana Popovici.
2020. "A Theoretical Framework for Estimating the Rate of Return to a Pharmacy Education Anywhere" *Pharmacy* 8, no. 3: 162.
https://doi.org/10.3390/pharmacy8030162