Capital Needs Analysis: How to Determine Your Business's Funding Requirements

Question 1: Income Troy and Kristy Need in Their First Year of Retirement 

Income needed by Troy and Kristy = current income x (1 + inflation rate) ^n 

Current income = $ 93,000 

Inflation rate = 2%  

Years to retirement = 8 years 

Income needed by Troy and Kristy = $ 93,000 x (1 + 0.02) ^8 

Income needed by Troy and Kristy = $ 93,000 x 1.171659381 

Income needed by Troy and Kristy on the first year of retirement = $ 108,964.32 

Question 2: What is the amount of capital necessary at the start of retirement to support their income needs throughout retirement? 

Amount of capital needed at the start of retirement = PV of an annuity of $ 108,964.32 

Real rate = (1 + interest rate after retirement)/ (1 + inflation growth rate) -1  

Interest rate after retirement = 6 %  

Inflation rate = 2% 

Real rate = (1 + 0.06)/ (1 + 0.02) -1  

Real rate = 1.0392 -1  

Real rate= 3.92%  

Amount of capital needed at the start of retirement = Annuity x (1 – (1 +r) ^n)/r 

Amount of capital needed at the start of retirement = $ 108,964.32 x (1-(1+ 0.0392) ^ -30)/ 0.092 

Amount of capital needed at the start of retirement = $ 108,964.32 x 17.4578 

Amount of capital needed at the start of retirement = $ 1,902,277.31 

Question 3: Personal Capital to Accumulate at Retirement at the age of 64 years 

Social Security benefit at 67 years = current value x (1 + inflation growth rate) ^ n  

  Number of years (n) = 67 years - 56 years  

Number of years (n) = 11 years  

Social Security benefit at 67 years = $ 30,000 x (1 + 0.02) ^ 11  

Social Security benefit at 67 years = $ 30,000 x 1.2433743084 

Social Security benefit at 67 years = $ 37,301.23 

PV of Social Security benefit at 67 years = SS benefit at 67 years x (1 – (1 +r) ^n)/r 

Number of years (n) = 30 years - 3 years = 27 years 

PV of Social Security benefit at 67 years = $ 37,301.23 x (1 – (1 + 0.0392) ^27)/ 0.0392 

PV of Social Security benefit at 67 years = $ 37,301.23 x 16.1441261883 

PV of Social Security benefit at 67 years = $ 614,505.17 

PV of Social Security benefit at 64 years = SS benefit at 64 years x 67 / (1+r) ^n 

Number of years (n) = 3 years  

PV of Social Security benefit at 64 years = $ 614,505.17x (1+ 0.0392) ^3 

PV of Social Security benefit at 67 years = $ 614,505.17x 1.122701563 

PV of Social Security benefit at 67 years = $ 547,555.55 

Personal capital required at 64 years = capital necessary at the beginning of retirement – PV of Social Security benefit at 64 years 

Personal capital required at 64 years = $ 1,902,277.31 - $ 547,555.55 

Personal capital required at 64 years = $ 1,354,721.76 

Question 4: Additional capital would they need to have accumulated at the time they retire at age 64? 

Additional capital accumulated = required amount / (1 + Nominal interest rate) ^ n  

Required amount = $ 2,000,000 

Nominal Interest rate = 6% 

Number of years = 30 years  

Additional capital accumulated = $ 2,000,000/ (1 + 0.06) ^ 30  

Additional capital accumulated = $ 2,000,000/5.7434911729 

Additional capital accumulated = $ 348,220.26182207 

Additional capital accumulated at retirement (64 years) = $ 348,220.26 

References 

Gohl, N., Haan, P., Kurz, E., & Weinhardt, F. (2020). Working life and human capital investment: Causal evidence from pension reform.