NPV is negative while benefit cost ratio is more than 1

[ibrahimecon]

Hi, I have calculated the net present value of a project and the benefit-cost ratio as well in R. While my net present value is negative (-300), my benefit-cost ratio is more than 1. I want to know if my code of calculating the benefit-cost ratio is correct or not.

I have calculated the npv using the following parameters and formula in R:

...

# plant info
q_fuel <- 398 #MLPY (million L/yr)
capex <- 422 #MM$ (million) capital exp (default value)
insurance_tax <- capex*.007
opex <- 372 #MM$/yr operating exp (default value)
hrs <- 8400 #hr/yr

# input info 
q_fd <- 0.9 #M t/yr (million tonnes annually)
q_water <- 1.6 #M t/yr 
q_elec <- 74.4 #M kWh/yr
q_gas <- 0.5 #M t/yr
q_h2 <- 0.01 #M t/yr
q_lab <- 12 #labor

p_fd <- 323 #$/t (default value)
p_water <- .57 #$/t
p_elec <- 0.11 #$/kWh
p_gas <- .8 #$/t
p_h2 <- 1210 #$/t (default value)
p_lab <- 0.043 #MM$/labor


# output info
q_jet <- 219 #MLPY (default value)
q_dsl <- 53 #MLPY (default value)
q_lpg <- 52	#MLPY
q_nap <- 63	#MLPY
q_meal <- 0.6 #M t/yr (default value)

p_jet <- 0.47 #$/L (default value)
p_dsl <- 0.82 #$/L
p_lpg <- 0.21	#$/L
p_nap <- 0.52	#$/L
p_meal <- 300 #$/t


# financial info
life <- 20 #yr
t_dep <- 7
t_loan <- 10 # loan term
r_inf <- 0.02
r_dis <- 0.10 # deflated discount rate (default value)
r_eq <- 0.15 # rate of return
r_tax <- 0.21


####################################### 
# NPV calculation
#######################################

# Set inflation rate to 2%
inflation_rate <- 0.02

# Calculate inflation factor for each year
inflation_factor <- (1 + inflation_rate)^(1:20)

CF0 <- capex*0.08*(1+r_dis)^2* inflation_factor[1]+capex*0.6*(1+r_dis)* inflation_factor[2]+capex*0.32* inflation_factor[3]

# Adjust expenses for inflation
exp_ut <- q_water * p_water* inflation_factor + 
  q_elec * p_elec* inflation_factor + 
  q_gas * p_gas* inflation_factor + 
  q_h2 * p_h2 * inflation_factor
exp <- exp_ut+q_fd*p_fd*inflation_factor+q_lab*p_lab*inflation_factor +insurance_tax*inflation_factor

sale_by <- (q_dsl*p_dsl+q_lpg*p_lpg+q_nap*p_nap+q_meal*p_meal)*inflation_factor


sale <- sale_by+q_jet*p_jet*inflation_factor
cat("revenue share for jet:",q_jet*p_jet*inflation_factor/sale,"\n")
cat("revenue share for dsl:",q_dsl*p_dsl*inflation_factor/sale,"\n")
cat("revenue share for lpg:",q_lpg*p_lpg*inflation_factor/sale,"\n")
cat("revenue share for nap:",q_nap*p_nap*inflation_factor/sale,"\n")
cat("revenue share for meal:",q_meal*p_meal*inflation_factor/sale,"\n")

ebitda <- sale-exp
#Calculate annual depreciation 
dep_per_year <- capex*.8/ t_dep
dep_schedule <- c(rep(dep_per_year, t_dep), rep(0, life - t_dep))
ebit <- ebitda - dep_schedule
amort <- amort.table(Loan=capex,n=t_loan,pmt=NA,r_dis)[["Schedule"]]

CF1 <- as.data.frame(amort) # cash flow for Y1-10
new_rows <- data.frame(Payment = rep(0, 10), 
                       `Interest Paid` = rep(0, 10),
                       `Principal Paid` = rep(0, 10),
                       Balance = rep(0, 10))

names(new_rows) <- names(CF1)

CF <- rbind(CF1, new_rows)
CF$Year <- 1:20

CF$EBIT <- ebit
CF$EBT <- CF$EBIT-CF$`Interest Paid`
CF$Depreciation <- dep_schedule
CF$Flow <- CF$EBT*(1-r_tax)+CF$Depreciation-CF$`Principal Paid`
CF$Discount <- r_dis
CF$PV <- CF$Flow/(1+CF$Discount)^CF$Year
NPV <- sum(CF$PV)-CF0
NPV

...

NPV is -383.2081 Million USD. Now, I want to calculate benefit-cost ratio. Benefit-cost ratio= pv of all benefits/pv of all costs

Now, I use the following code ti calculate benefit-cost ratio:

...

# Calculate the present value of benefits
benefit <- sum(sale-CF$`Interest Paid`*(1-r_tax)-CF$`Principal Paid`/(1+CF$Discount)^CF$Year)


# Calculate the present value of costs
cost <- sum(exp-CF$`Interest Paid`*(1-r_tax)-CF$`Principal Paid`/(1+CF$Discount)^CF$Year)



bcr <- benefit/cost
bcr

...

The benefit cost ratio is 1.18. I tried the following code:

...

# Calculate the present value of benefits
benefit <- sum(sale/(1+CF$Discount)^CF$Year)


# Calculate the present value of costs
cost <- sum(exp/(1+CF$Discount)^CF$Year)



bcr <- benefit/cost
bcr =1.17

...

So i have a negative net present value, but the benefit-cost ratio is more than 1. How is that possible? do I have anything wrong in my formula of calculation of the benefit-cost ratio? for example, maybe i should not add everything (1-r_tax, interest and payment) in both the benefit and cost side? How do I correctly account for all of these (1-r_tax, and interest and payment) when I calculate the benefit-cost ratio, please?

[nirgrahamuk]

It might be helpful for you to know how to properly format code and console output that you post here. Using proper code formatting makes the site easier to read, prevents confusion (unformatted code can get garbled by the forum software ), and is generally considered the polite thing to do. Check out this FAQ to find out how — it's as easy as the click of a button! :

FAQ: How to format your code

Formatting Code: the Basics All code or console output you include in your posts should be formatted properly. Luckily, this is very easy to do! Just use the code formatting button at the top of the post editing box: [image] Select some code Click the </> button! The code formatting button automatically adds special Markdown formatting symbols to whatever you selected. If you check the preview pane to the right of your post, you'll see that the forum software now outputs nicely formatted code . [04] The code formatting button is pretty smart! It can tell the difference between snippets of code that are part of a sentence and blocks of code that stand alone. …

[ibrahimecon]

Thank you. Edited it now, hope its fine now

[nirgrahamuk]

this seems more like an accounting problem than an R one persay ?
I dont have answers but I do have questions...
Is it correct the depreciation is the deposit schedule ?
does it make sense that if we adjust the depreciation to zero throughout he NPV becomes much lower than with it in there ?

[ibrahimecon]

The depreciation is considered straight-line depreciation, so for all the depreciation periods (say 10 years), depreciation is the same but if the lifetime of the project is 20 years, for the last 20 years, depreciation is zero. But changing depreciation does not really change much of the calculations